# IV Stability and Control Processes

# Conference

## in memory of Prof. Vladimir Zubov

## Saint Petersburg, Russia

5-9 October 2020

Submit contribution# Scientific Program

## Call for Papers

- Stability
- Methods of Lyapunov Functions
- Dynamic Systems Theory
- Mechanical Systems Control
- Control and Optimization of Electro-Physical processes
- Game Theory. Conflict Systems Control
- Methods for Analysis and Design of Systems with Time-delay
- Robust Control
- Optimization Methods
- Non-Linear Mechanics and Solid-state Physics
- Socio-economic Systems Control
- Medical and Biological Systems Control
- Informatics and Control Processes
- Mathematical Modelling and Image Processing Methods
- Artificial Intelligence

## Conference Agenda

Conference working language is **English**.

The conference program will contain invited and regular oral presentations.

The length of keynote and invited talks is 50 mins, regular presentation is 15 mins.
The sessions will take place on-line in Zoom.
Please download and install it in advance. You can find "how to" in Zoom here https://zoom.us/resources

## Conference Schedule

The time is in MSK (UTC/GMT +3 hours) timezone.

#### Opening Session

##### Leon Petrosyan, Joachim Knebel, Dmitri Ovsyannikov, Anna Golovkina

Welcoming words from the SCP Program Committee.

#### A Dynamical System View on Nonlinear Optimal Control Analysis and Design

##### Noboru Sakamoto

This note presents a view from the theory of dynamical system, such as invariant manifolds and lambda-lemma, for the analysis and the design of optimal control for nonlinear systems. The optimal control problems considered are optimal stabilization and optimal transfer problems. The theory of stable manifold and its iterative computation play the central role for the optimal stabilization design and the lambda-lemma which describes the flows around the invariant manifolds is used for analysis of the optimal transfer problem including turnpike property in the optimal control system.

#### Adaptation and Learning: A Brief History

##### Alexander Fradkov

Machine learning and artificial intelligence have attracted a lot of attention during recent years. They are applied to various new problems and it looks like they are based upon completely new ideas in the applied science. However there exist strong links between machine learning and classical adaptation methods which are much lesser known and almost not exploited nowadays. In this talk a brief overview of the historical evolution of the machine learning field and its relations to adaptation, optimization and adaptive control are discussed. A number of little-known facts published in hard-to-reach sources are presented.

#### Mechanical Systems Control, Part 1

##### Session Mo1A. Chair: Alexander Shmyrov

Location: Zoom ID: 960 0377 9810https://youtu.be/LpsguXYf1OI

**ID 073: Representation Forms of the Angular Velocity Vector for an Orthonormal Basis of a Moving Frame **

**Vladislav S. Ermolin, Tatyana V. Vlasova**

In this paper, we consider a Cartesian moving reference frame.
Its angular velocity vector is introduced as a solution to a system of kinematic equations of basis vectors.
These equations connect the position of the basis vectors with their velocity. The construction of a formula
for the angular velocity vector of an orthonormal basis is described. It is shown that the angular velocity vector
in the found form is a solution to the system of the equations. Using transformations of the constructed solution,
four more representation forms of the angular velocity vector are derived. It is shown that all the obtained forms
define the same angular velocity vector of the moving space, though they contain different elements. All of the forms
are also solutions of the system of kinematic equations. Presented results can be applied both to a solid body and to any rigid system.

**ID 131: Space Robot Control System for Long Distances**

**Polina Efimova
**

The article proposes a new approach to control of a space robot at large distances.
A key feature of the method is to perform the necessary operations off-line using an auxiliary ground robot.
This method allows to minimize the effect of delays in signal transmission due to features in the control algorithm.
Using of feedback on force is necessary for the interaction space robot with objects having holonomic constraints,
which is typical for assembly operations. The article gives a mathematical description of the elements of the bilateral control
system and also presents a method of adaptation of the robot to environmental changes.

**ID 125: Attitude Controlled Motion in a Neighborhood of the Collinear Libration Point L_1
**

**Dzmitry Shymanchuk, Vasily Shmyrov, Alexander Shmyrov
**

This paper considers an attitude controlled motion of a celestial body within the restricted three-body problem of the Sun-Earth system. The equations of the attitude controlled motion in a neighborhood of the collinear libration point L1 are investigated. The attitude controlled motion is described using the Euler's dynamic equations and the quaternion kinematic equation. We investigate the stability problem of the celestial body attitude motion in relative equilibrium positions and programmed attitude motions with proposed control laws in the neighborhood of the collinear libration point L1. To study stabilization problem, Lyapunov function is constructed in the form of the sum of the kinetic energy and special ``kinematic function'' of the Rodriguez-Hamiltonian parameters.

**ID 143: An Embedded Explicit Method for Partitioned Systems of Ordinary Differential Equations
**

**Alexey Eremin, Igor Olemskoi
**

In the paper an explicit Runge--Kutta type method for partitioned systems of ordinary differential equations is considered. The partitioning is made on base of structural properties of the system right-hand side functions. With use of such properties an explicit method that requires fewer stages than classic Runge-Kutta method application to systems of ordinary differential equations do. A system of order conditions for an embedded pair of methods of orders six and four is presented. Coefficients of such pair of methods that provide a convenient local error estimation to organize a variable time-step procedure is constructed. Numerical testing of the constructed method an its comparison to widely used Dormand-Prince pair of orders six and five is held. The test results confirm the better performance of the constructed method in sence of global error to amount of right-hand side evaluations ratio.

#### Socio-Economic Systems Control, Part 1

##### Session Mo1B Chair: Dmitriy Gromov

Location: Zoom ID: 949 2440 0195, https://youtu.be/yF_BpBg2jek

**
ID 184: Queueing Systems with Opposite Queues
**

**
Anastasiya Glushakova, Alexander Kovshov
**

The queueing system with one server and two arrival streams is under consideration. Arrival streams are independent and Poisson with different rates. Thus, the queueing system accepts two types of jobs. If the server is busy, jobs are sent to the queue. Each job type has its own queue and waiting room.
The server can serve two jobs simultaneously. In this pair of jobs, one job must be of the first type, and the other must be of the second type.
The server cannot serve only one job, and it cannot serve two jobs of the same type. The service time is distributed exponentially. In this research,
formulas were obtained that calculate the probability of all states of the system for two particular cases. Two computer programs were created that
calculate the probabilities of all states of the system in the general case.

**
ID 091: Choice Modeling in Insurance
**

**Alexandr Sachkov
**

Choice problems arising in modern insurance are considered in this article. After introducing all the necessary concepts, two distinct approaches to modeling choice are discussed: actuarial science and its instruments, along with axiomatic choice theory. Afterwards, one relevant example is analyzed and both approaches are shown in action. Lastly, some conclusions are drawn and potential further research directions are given.

**
ID 046: Supply Chain Model with Random Demand
**

**
Sergei Kalin, Elena Lezhnina, Tatyana V. Vlasova
**

The ability to timely and efficiently satisfy customer requests is
one of the most important competitive advantages of any organization.
A valuable and effective tool to achieve this is the competent modeling and optimization of supply chains.
Modeling is complicated by the often encountered combination of external and internal uncertainties, which significantly
affects the planning of the optimal allocation of resources. In this paper, we solve the problem of constructing an optimization
model of a supply chain with random demand, close to real life. A supplychain model with external and internal uncertainty was built
and checked for correctness. In the paper we model all stages of production taking into account the randomness of demand and possible
disraptions at every stage.

**
ID 066: Structural Analysis of Directed Signed Networks
**

**
Elizaveta Evmenova, Dmitry Gromov
**

Signed networks represent a particularly interesting class of complex networks with many applications in sociology,
recommender and voting systems. There are a couple of theories developed for the description of the structure of such networks,
including the structural balance, status and sentiment analysis. Most results devoted to signed networks are based on the
assumption that the network under study is undirected. In this contribution we present initial results aimed at quantifying
the amount to which real directed networks differ from undirected ones. We carry out our analysis for the network describing
the Wikipedia adminship elections.

#### Methods for Analysis and Design of Systems with Time-Delay, Part 1

##### Session Mo2A. Chairs: Vladimir Rasvan, Alexey Zhabko

Location: Zoom ID: 960 0377 9810, https://youtu.be/LpsguXYf1OI

**ID 102: An Algorithm for Solving Local Boundary Value Problems with Perturbations and Delayed Control**

**Alexander Kvitko, Alexey Eremin, Oksana Firyulina**

In the paper a class of controllable nonlinear stationary systems of ordinary differential equations with account of external perturbations is studied. The control function has a delay and is norm-bounded. A control transferring the system from a given initial state to an arbitrary neighborhood of the origin is constructed. The algorithm has both numerical and analytical stages and is easy to implement. A Kalman-type constructive sufficient condition under which the transfer is possible is presented. The algorithm efficiency is demonstrated with solving a robot-manipulator control problem.

**
ID 166: The Prediction Scheme to the Linear Systems with Linearly Increasing and Constant Delays
**

**Alexey Zhabko, Olga Chizhova, Oleg Tikhomirov
**

Mathematical models of dynamic processes described by systems of differential-difference equations of delay type with constant input delay and unbounded state delay are considered. Such a class of systems has been investigated significantly worse than the class of systems with both constant aftereffects. However, the state time-delay is not always constant. In recent times, many new applications have appeared in the controlled dynamic processes described by systems with time-dependent delays. This paper is devoted to the study of the stabilization problem of the linear differential-difference systems with linearly increasing state delay and constant input delay. The theoretical basis of the study is prediction scheme for the compensation of the state delay in the construction of stabilizing controller. The possibility of construction such a control has been studied and some sufficient conditions of the asymptotic stability of the close-loop system have been obtained.

**ID 213: The Generalized Myshkis Problem for a Linear Time-Delay System with Time-Varying Delay
**

**
Alexey Egorov
**

A time-delay linear system with time-varying delay is investigated. The delay is bounded by a fixed constant. The generalized Myshkis problem for this system has been formulated. This problem consists in finding such values of parameters that the system is uniformly stable for any admissible delay. Two sufficient conditions for solvability of this problem are given. First condition is less conservative, but hard to check, whereas the second condition is presented in the form of quadratic convex optimization task.

** ID 188: On the Stability of Linear Time Delay Systems With Arbitrary Delays
**

**
Irina Alexandrova, Sabine Mondie
**

The construction of Lyapunov - Krasovskii functionals with prescribed derivative for linear time-invariant time delay systems is based on the Lyapunov matrix. This matrix is usually computed with the help of the so-called semianalytic procedure, which is to solve a system of ODE with the boundary conditions. The problem lies in the fact that the dimension of this ODE system may be large in some cases. Moreover, the semianalytic procedure is not applicable in the case when the delays in the system are incommensurate. This is the case addressed in the contribution. We suggest the stability conditions for systems with incommensurate delays which do not require computation of the Lyapunov matrix in this difficult case. The Lyapunov matrix of another system with commensurate delays, for which the semianalytic procedure is applicable, is involved instead. The implementation issues of the method are discussed, and the illustrative example is given.

#### Nonlinear Mechanics and Solid-State Physics, Part 1

##### Session Mo2B. Chairs: Yulia Pronina and Mikhail Grekov

Location: Zoom ID: 949 2440 0195, https://youtu.be/yF_BpBg2jek

**ID 127: Elastic-Plastic Bending of Vertical Supports of Drilling Platforms
**

**Natalia Naumova, Galina Pavilaynen, Denis Ivanov
**

Bending of vertical beams with the SD-effect and own weight under a constant moment
or a concentrated load at the end of the beam is considered. The constant moment simulates
the pressure of a uniform ice field, and the concentrated load simulates the pressure of an
iceberg or ice hummock. To solve this problem, the Ilyushin model of perfect plasticity is
used. The problem is solved analytically and numerically. As an example the bending of the
beam with the SD-effect, own weight and hydrostatic pressure is considered. The material
of the beam is a steel A40X. The classical solutions for isotropic beam and beam made of
material with the SD-effect are compared with soft package COMSOL.

**
ID 169: Stress Analysis in a Spherical Pressure Vessel with Multiple Notches
**

**Olga Sedova, Daria Okulova
**

A finite element analysis of a thin-walled sphere under internal pressure with defects on its outer surface is conducted. The defects are modelled as spherical notches of the same size. Uniform and random arrangement of notches along the equator of the sphere is considered. The distribution of the maximum stress near defects is obtained for the different numbers of defects.

**ID 008: Interaction of Finite Amplitude Surface Waves in a Basin with a Floating Elastic Plate
**

**
Anton Bukatov
**

On the basis of multiple scales method, a solution of the problem about progressive surface waves nonlinear interaction in a finite depth basin with a floating elastic plate is constructed. Asymptotic expansions are obtained up to the third order of smallness for the velocity potential of liquid particles movement and elevation of the plate - fluid surface. The analysis of the dependence of the dispersion properties of the formed disturbance on the elastic and mass characteristics of ice plate, its longitudinal compression, is carried out. The influence of nonlinearity of vertical displacements acceleration of the elastic ice plate on the fluctuations amplitude-phase characteristics is studied. It is shown, that the presence of compressive force is expressed in the lag of the fluctuation phase from the phase obtained in the absence of compression.

** ID 041: Surface Dislocation Interaction by the Complete Gurtin-Murdoch Model
**

**
Mikhail Grekov, Tatiana Sergeeva
**

The interaction of an edge dislocation array with a free surface of an elastic solid is considered within the framework of the complete Gertin--Merdoch surface elasticity model. The generalized Young--Laplace boundary equation of the plane elasticity problem is derived in terms of complex variables for the general case of a curvilinear cylindrical surface. Using this boundary equation in the case of a line edge dislocation array placed near the planar surface, the solution of the corresponding boundary value problem is reduced to the integro-differential equation in the unknown complex displacement. Based on the analytical solution of this equation in terms of complex Fourier series, we present the numerical results for the stress field at the surface and discuss the difference them from those obtained with the simplified Gertin--Merdoch models.

#### Methods for Analysis and Design of Systems with Time-Delay, Part 2

##### Session Mo3A. Chairs: Vladimir Rasvan, Alexey Zhabko

Location: Zoom ID: 960 0377 9810, https://youtu.be/LpsguXYf1OI

**ID 145: Fourth Order Method for Differential Equations with Discrete and Distributed Delays
**

**Aleksandr Lobaskin, Alexey Eremin
**

Differential equations with discrete and distributed delays are considered. Explicit continuous-stage Runge-Kutta methods for state-dependent discrete delays based on functional continuous methods for retarded functional differential equations and Runge-Kutta methods for integro-differential equations based on methods for Volterra equations are combined to get a method suitable for both types of delays and converging with order four. A method that requires six right-hand side evaluations and only two its integral argument evaluations is presented. The questions of the practical implementation for delay differential equations with in general non-smooth solution are discussed. The numerical solution of test problems confirms the declared fourth order of convergence of the constructed method.

**
ID 174: On Asymptotic Quiescent Position in Time Delay Systems
**

**Svetlana Kuptsova, Sergey Kuptsov, Uliana Zaranik
**

The nonlinear time-delay systems are considered and the limiting behavior of their solutions is investigated. The case in which the solutions have the trivial equilibrium that may not be an invariant set of the system is studied. The Lyapunov-Krasovskii functionals approach is applied to obtain sufficient conditions for the existence of an asymptotic quiescent position in the large. In the case when a general system has a trivial solution, new sufficient conditions for its asymptotic stability are obtained. Examples, that illustrate the application of the obtained results, are given.

#### Nonlinear Mechanics and Solid-State Physics, Part 2

##### Session Mo3B. Chairs: Yulia Pronina and Mikhail Grekov

Location: Zoom ID: 949 2440 0195, https://youtu.be/yF_BpBg2jek

**ID 094: On Minimization of Metal Costs for a Pipeline Exposed to External Corrosion Under Pressure
**

**Marina Elaeva, Yulia Pronina, Sergey Kabrits
**

The paper concerns the problem of minimization of metal consumption for a pipeline with unlimited service life and the possibility to replace its parts, without re-use of the material of the old parts replaced. The pipeline is exposed to external mechanochemical corrosion under pressure. The presence of a protective film and corrosion inhibition are taken into account. The problem is reduced to finding the minimum of the corresponding objective function. For an uncoated pipe, this function has only one minimum at a relatively large initial thickness, which cannot always be set in practice for technological reasons. In such cases, it is more advantageous to set the initial thickness of the pipe as large as possible for a specific manufacturing technology. For pipes with coatings, the objective function may have two points of the local minimum: at the minimal allowable thickness and at a relatively large one.

**
ID 128: Sommerfeld Effects in Two Mass Crusher with 3 Degrees of Freedom
**

**Serge Miheev, Petr Morozov
**

The crushing process in a vibration two-mass crusher with mechanical restrictions of degrees of freedom up to 3 and with an asynchronous engine as an unbalance drive is considered. The system of ordinary differential equations that accurately describes the dynamics of the device at idle
to go is applied. To simulate the stroke, this system was transformed into a system of stochastic differential equations.
The analysis of the crushing process parameters was made at various rotational frequencies of the magnetic field of the asynchronous drive.
The frequencies at which the Sommerfeld effect is manifested are established.

#### From Control Invariant Sets to an Inverse Optimality Perspective on the Constrained Control Design

##### Sorin Olaru

The paper aims to review some of the early works on constrained control underlining their influence on the recent development of optimization-based control design. We will trace the path (mainly within a linear time-invariant framework) from vertex controllers, to model-based predictive control and ultimately to interpolation-based control. Interestingly, we will point to the relationship between these techniques and the performance indexes in optimal-control design. On their turn, the performance indices can be seen as candidate Lyapunov functions but can also be interpreted in a geometrical perspective as convex liftings over the controllable regions of the state space. This last perspective provides a link to the inverse optimality argument for any stabilizing control law. Finally, we will point to the parameter uncertainty in dynamical models as part of such an inverse-optimal control policy and discuss some open problems.

#### Mechanical Systems Control, Part 2

##### Session TuA1. Chair: Alexander Kosov, Dmitri Shimanchuk

Location: Zoom ID: 976 2747 8439, https://youtu.be/sL8rv8wKazU

**ID 140: Construction of Connecting Trajectories in the Circular Restricted Three-Body Problem
**

**Vasily Shmyrov, Dzmitry Shymanchuk, Alexander Shmyrov
**

In this paper, we consider the problem of construction of the connecting trajectories between a neighborhoods of collinear libration points of the Sun-Earth system. The motion of spacecraft in these regions of space is described using the equations of the circular restricted three-body problem and with help of Hill's model. At the first stage, such trajectories are constructed using the symmetry properties that the Hill's model possesses. Further, the obtained trajectories are modeled in a circular three-body problem.

**
ID 146: Constructing a Polynomial Method in the State Space for a Nonlinear Optimal Control Problem
**

**Daniel Zlobin, Dzmitry Shymanchuk
**

The paper presents a method for taking into account phase constraints and control constraints in the direct construction of a quasi-optimal polynomial trajectory in the state space of a system of a special form, the left-hand side of which preserves the polynomiality of the input arguments, and the right-hand side contains an orthogonal linear control transformation parameterized by the trajectory, which allows one to exclude control from tasks and build a trajectory directly in the state space. To take into account the phase constraints, we use an asymptotically exact monotone estimate of the range of values of the polynomial based on the expansion in Bernstein polynomials. Boundary conditions are taken into account using the Hermite polynomial. The presented method can also be applied to complex systems provided that they are approximated. The presented method is illustrated by the example of the task of terminal control of an aircraft.

**
ID 108: About Controlled Motion of Spacecraft with a Solar Sail
**

**Elena Polyakhova, Vladimir Korolev, Nikolai Stepenko, Irina Pototskaya
**

The features of translational and rotational motion of all parts of the structure for controlling the solar sail of a Spacecraft are considered, which take into account the possibility of changing the size, shape, surface properties or orientation of the sail elements relative to the flux of sunlight. The main factor is taking into account the current position in orbit to control the rotation of the spacecraft relative to the selected axes.
To control the motion of a spaceship, we can change the size, shape, surface properties, or orientation of sail elements relative to the flow of sunlight. The equations of motion can be represented on the basis of the model of the problem of two bodies moving in a gravitational field, taking into account perturbations.
The stability of the orientation of the spacecraft sail system is ensured by the moments of forces relative to the center of mass.

**
ID 047: Boundary Control of String Vibrations with Given Values of the Deflection Function at Intermediate Moments of Time
**

**
Vanya Barseghyan
**

A boundary control problem for the string vibration equation with given initial and terminal conditions and with given values of the deflection function of the string points at intermediate moments of time is considered. The problem is reduced to a problem with zero boundary conditions and further using the variable separation method, the problem is reduced to a control problem with a countable number of ordinary differential equations with given initial, terminal, and multipoint intermediate conditions. In practice, the modal method is widely used on the basis of which the problem is solved for arbitrary numbers of the first harmonics. In this paper, employing methods of control theory for finite-dimensional systems, a control action for arbitrary numbers of the first harmonics is constructed. The approach proposed for the string vibration equation allows usage for other (not one-dimensional) vibrational systems.

#### Nonlinear Mechanics and Solid-State Physics, Part 3

##### Session TuB1. Chair: Mikhail Grekov, Sergey Kostyrko

Location: Zoom ID: 927 1562 0438, https://youtu.be/asZ7DLhc49Y

**ID 018: A Rectangular Prism under Own Weight: Comparison of the Method of Initial Functions and the Finite Element Method
**

**Guriy N. Shirunov, Alexander V. Matrosov, Denis A. Sarvilin
**

In this paper we study the bending of a massive elastic linearly deformable body under its own weight. Two approaches are analyzed: analytical one based on the method of initial functions (MIF) and numerical one based on finite element modeling (FEM).
An algorithm for constructing a general solution for a linearly elastic parallelepiped using the superposition method based on three MNF solutions is described. The results of analyzing of a massive bridge using two approaches are presented. The advantages and disadvantages of the analytical approach proposed and numerical modelling are analyzed.
Inaccurate satisfaction of the boundary conditions on the horizontal load-free faces when using the FEM is noted. The inability of the FEM to track some of the nuances in the behavior of shear stresses on clamped faces is also noted.

**
ID 068: On Edge Effect for a Finite Doubly Periodic System of Perpendicular Cracks
**

**Abdulla Abakarov, Yulia Pronina
**

The aim of the work was to assess the minimum size of a finite doubly periodic square array of cracks in an infinite plane so that the fracture characteristics in the center of this array would hardly change with its further increase. For this purpose we investigated the influence of the size of the crack array on the energy release rate near the central (and side) cracks for various types of loading: uniaxial and biaxial tension and in-plane shear. We also observed the effect of the crack density on the relative change in the energy release rate with the increase in the number of cracks.

**
ID 122: Wave Motions of Liquid with Consideration of the Density Diffusion
**

**Sergey Peregudin, Elina Peregudina, Svetlana Kholodova
**

Waves of small amplitude in a~stratified liquid are considered.
The original physical problem is described by the system of partial differential equations with corresponding boundary-value conditions.
We further study linearized free-wave problems in a stratified liquid, problems of internal waves in a~rotating stratified liquid, problems of forced internal waves in a~rotating stratified liquid, and problems of free internal waves in the presence of horizontal density diffusion.
The results obtained can be applied in problems of hydrodynamics, theory of waves, geophysics,
applied mathematics, marine construction at the design stage, and in marine wave suppression problems.

**
ID 087: Large Deformations of a Plane with Elliptical Hole for Model of Semi-Linear Material
**

**
Yulia Malkova, Venyamin Malkov
**

The exact analytical solution of the nonlinear problem of elasticity for a
plane with an elliptical hole is obtained for semi-linear material. External load are
constant nominal (Piola) stresses at infinity, the boundary of a hole is free.
The complex variable formulation and conformal mapping technique are used.
The hoop stress distribution along the boundary of a hole is analyzed for the case, when the material is deformed by uniaxial
tension/compression. A comparison is made with the stresses of a similar linear problem.

#### Mechanical Systems Control, Part 3

##### Session TuA2. Chair: Alexander Kosov, Dmitri Shimanchuk

Location: Zoom ID: 976 2747 8439, https://youtu.be/sL8rv8wKazU

**ID 211: Vibration Control of a Non-homogeneous Circular Thin Plate
**

**Andrei Smirnov, Grigorii Vasilev
**

Transverse vibrations of an inhomogeneous circular thin plate are studied. The plates, which geometric and physical parameters slightly differ from constant and depend only on the radial coordinate, are analyzed. After separation of variables the obtained homogeneous ordinary differential equations together with homogeneous boundary conditions form a regularly perturbed boundary eigenvalue problem. For frequencies of free vibrations of a plate, which thickness or Young's modulus nonlinearly depend on the radial coordinate asymptotic formulas are obtained by means of the perturbation method.
The effect of the small perturbation parameter on behavior of frequencies is analyzed under special conservation conditions:
i) for a plate, the mass of which is fixed, if the thickness is variable and ii)
for a plate with the fixed average stiffness, if Young's modulus is variable.
Asymptotic results for the lower vibration frequencies well agree with the results of finite element analysis with COMSOL Multiphysics 5.4.

**
ID 180: On the Movement of Gyrostat Under the Action of Potential and Gyroscopic Forces
**

**Alexander Kosov, Edward Semenov
**

A system of differential equations describing the movement of a gyrostat under the action of potential and gyroscopic forces is considered. The type of moment of forces at which the system has the three first integrals is specified. For the analog of the Lagrange case, integration in quadratures is performed. Analogs of the case of complete dynamic symmetry and the Hess case are also indicated. Based on the optimal damping principle proposed by V.I.Zubov, the design of a control moment created by circular-gyroscopic forces and providing the output of one of the coordinates to a constant (although unknown in advance) value or the transition of the state vector to the surface of the level of the Hess partial integral is offered.

**
ID 063: Resonant Oscillations of a Controlled Reversible Mechanical System in the Vicinity of Equilibrium
**

**Valentin Tkhai, Ivan Barabanov
**

A reversible mechanical system in the vicinity of equilibrium is considered. It is assumed that the linear approximation matrix has a pair of purely imaginary eigenvalues with the frequency $\omega$; other eigenvalues are not multiples to the above one and are different from zero. We study the system's oscillations under the action of periodic controls with a frequency of $2\pi/\omega$ and a small gain of the regulator $k$. The existence of various resonant oscillations of the controlled system is established, and the amplitudes of the oscillations are estimated in terms of the parameter $k$.

**
ID 101: Algorithm for Navigating Mobile Robots in a Limited Set of Sensors
**

**
Viktor Fedorov
**

Nowadays, automation of processes in which a robot can replace a human is widespread. To solve this problem, robots must be able to move independently from one position to another. One of the most effective methods for solving a navigation problem is the method of constructing a navigation system based on the simultaneous localization and mapping algorithm and obstacle avoidance algorithms. One of the most effective obstacles avoidance algorithms is the D-star algorithm, which, despite its effectiveness, has some drawbacks. This modification allows to eliminate some problems arising during the implementation of the navigation system.

#### Nonlinear Mechanics and Solid-State Physics, Part 4

##### Session TuB2. Chair: Mikhail Grekov, Sergey Kostyrko

Location: Zoom ID: 927 1562 0438, https://youtu.be/asZ7DLhc49Y

**ID 098: Stability Analysis of Nanopatterned Bimaterial Interface
**

**Gleb Shuvalov, Sergey Kostyrko
**

In this paper, it is shown that the nanopatterned interface of the heteroepitaxial material system is not stable due to the diffusion atom flux along the interface. The main goal of this research is to analyze the conditions of interface stability. To this end, we developed a model coupling thermodynamics and solid mechanics frameworks. Within the Gurtin--Murdoch theory of surface/interface elasticity, the interphase between two materials is considered as a negligibly thin layer with the elastic properties differing from those of the bulk materials. The growth rate of interface roughness depends on the variation of the chemical potential at the curved interface, which is a function of interface and bulk stresses. The stress distribution along the interface is found from the solution of plane elasticity problem taking into account plane strain conditions. After that, the linearized evolution equation is derived, which describes the amplitude change of interface perturbation with time.

**
ID 096: Interaction of Misfit Dislocations with Perturbated Surface in Epitaxial Thin Film
**

**Sergey Kostyrko, Mikhail Grekov, Takayuki Kitamura
**

The analytical method for the analysis of the stress fields arising as a result of interaction of misfit dislocations with an undulated surface in an epitaxial thin film is considered. The boundary value problem of the plane theory of elasticity for an infinite isotropic half-space containing an infinite row of line edge dislocations paralel to the undulated boundary is formulated assuming that the elastic properties of the film and substrate materials are approximately equal. The depth of dislocations beneath the surface is equal to the film thickness, and dislocations are spaced with the distance equal to the surface perturbation wavelength. The solution is based on Goursat--Kolosov's complex potentials, Muskhelishvili's representations, the boundary perturbation method and superposition technique. Using the first-order approximation of the boundary perturbation method, the hoop stress distribution along the sine-curved surface is analyzed by varying the distance of dislocations to the boundary.

**
ID 148: On the Account of Transverse Young-Laplace Law Under Stability of a Rectangular Nano-plate
**

**Anatolii Bochkarev
**

As known, the constitutive relations of the Gurtin–Murdoch model of the surfaces elasticity take into account both elastic properties of a solid and surface tension of a liquid. Previously, most authors believed that, surface tension does not significantly affect the mechanical properties of a thin-walled elastic nano-objects and therefore it either was not or only in-plane taken into account, ignoring the Young-Laplace law in the transverse direction. In the present work, on the basis of the nonlinear representation of the surface tension obtained earlier, the structure of the strain energy of a nano-plate is substantiated, taking into account the surface tension in both tangential and transverse directions. Using the example of compressive buckling of a nano-plate, it is shown that the accounted surface tension terms can increase the size effect of the critical load by up to 80%.

**
ID 017: Analytical Solutions for Cylindrical Bending of Multilayered Orthotropic Plates
**

**
Alexander V. Matrosov, Dmitry Goloskokov
**

This work is devoted to the study of the application of two analytical solutions of the cylindrical bending of orthotropic plates for the analysis of layered structures. The first one is the famous Pagano's solution and the second one is a solution obtaned by a method of initial functions (MIF). It is shown that when applying the Pagano solution, the resolving system of linear algebraic equations depends on the number of layers in the structure. When using the MIF solution, the resolving linear system always has a second order. It is noted that this fact is associated with arbitrary constants in the two solutions obtained: in the Pagano solution, they have no mechanical meaning, and in the MIF solution they represent displacements and stresses on the initial line. The results of calculations of multilayer composites and the time of their execution for two investigated solutions are presented.

#### Stability, Part 1

##### Session TuA3. Chair: Alexander Aleksandrov, Alexey Platonov

Location: Zoom ID: 976 2747 8439, https://youtu.be/sL8rv8wKazU

**ID 088: Study of the Stability Features of Solutions of Systems of Differential Equations
**

**Gennady Ivanov, Gennady Alferov, Vladimir Korolev, Dzmitry Shymanchuk
**

The stability conditions for solutions of systems of ordinary differential equations are considered. The conditions and criteria for the use of partial and external derivatives are proposed. This allows us to investigate the behavior of a function of several variables, without requiring its differentiability, but using only information on partial derivatives. This reduces the restrictions on the degree of smoothness of the studied functions.
The use of the apparatus of external derived numbers makes it possible to reduce the restrictions on the degree of
smoothness of manifolds when studying the question of the integrability of the field of hyperplanes.
Using the apparatus of partial and external derived numbers, it can be shown that the investigation of the stability of solutions of
a system of differential equations can be reduced to an investigation of the solvability of a system of equations of a special form.

**
ID 002: Diagonal Riccati Stability of a Class of Complex Systems and Applications
**

**Alexander Aleksandrov, Nadezhda Kovaleva
**

The problem of diagonal Riccati stability is studied for a class of complex systems describing interaction of the second-order subsystems. It is assumed that the connection graph has a special structure and there is a constant delay in connections between the subsystems. Conditions under which the problem of diagonal Riccati stability for an original system can be reduced to that one for an auxiliary positive system are derived. If the auxiliary systems are diagonally Riccati stable, then there exist diagonal quadratic Lyapunov–Krasovskii functionals ensuring that zero solutions of the original complex systems are exponentially stable for any nonnegative delay. To demonstrate the effectiveness of the obtained results, some applications of the developed approaches to the stability analysis of mechanical and biological systems are presented.

**
ID 190: An Estimation Extension of Domain of Attraction for Second-Order Dynamic Systems
**

**Kirill Postnov
**

In this paper we offer a method for extension of estimation of domain ofattraction (DA) for autonomous nonlinear dynamical system defined on a plane. Weconsider an estimate of domain of attraction obtained by the Zubov’s method anddescribe the technique of estimation extension using the geometric properties of avector field. A numerical example illustrates the feasibility of the proposed method.

**
ID 012: Economic Evolution with Structural Variations
**

**
Alexander Kirillov, Alexander Sazonov
**

In this paper, an approach to mathematical modeling of the Schumpeterian theory of the endogenous evolution of the economic systems is presented. In section 2 the model of the sector capital distribution dynamics over efficiency levels
is proposed. In order to take into account the boundedness of the economic growth the notion of economical niche volume is introduced. The global stability of the presented dynamical system is proved. In section 3 the approach to the modeling of the structural variations on the base of the system with
the variable number of the efficiency levels is presented. The scenarios of the emergence and vanishing of the efficiency levels are proposed. Some results concerning the dynamics of the special discrete system describing the efficiency levels presence are obtained. The proposed models permit to evaluate and predict the dynamics of the efficiency levels of the economic sector firms development.

**ID 001: On the Stability of Nonlinear Mechanical Systems with Time-Varying Discontinuous Coefficients
**

**
Alexey Platonov
**

In the paper, one class of mechanical systems with nonlinear force fields is considered. It is assumed that the system is under influence of dissipative, gyroscopic and potential forces. Moreover, we suppose that there is a non-stationary coefficient at potential forces. The case where this coefficient is piecewise continuous and piecewise monotonous on any finite time interval is investigated. Thus, the system can be considered as a non-stationary switched system. We study the situation where this coefficient can be unbounded. Stability conditions for such class of systems are obtained. The Lyapunov direct method is used. Both multiple Lyapunov functions and single Lyapunov functions are constructed. Some examples are presented to illustrate the results.

#### Socio-Economic Systems Control, Part 2

##### Session TuB3. Chair: Alexander Prasolov, Nikolay Smirnov

Location: Zoom ID: 927 1562 0438, https://youtu.be/asZ7DLhc49Y

**ID 003: On Depth of Immersion in Forecasting Task
**

**Alexander Prasolov, Nikita Ivanov
**

The forecast of dynamic processes is based on mathematical models which usually describe determinate and stochastic characteristics of processes adequately. Parameters values of considered models are estimated by observation data over the processes in the past. It often occurs that there is data excess, which means that additional number of data does not contribute to the precision of forecasting but makes it more expensive. This work is devoted to the estimation of forecasting depth at the fixed horizon. It was assumed that time series, of which forecast is considered, possess some informative features that allow establishing the balance between the horizon and the depth of the forecast. The algorithm of depth estimation has been offered and real non-stationary time series has been analyzed. This analysis demonstrated that there exists quasi-optimal depth for fixed horizon of forecasting.

**
ID 049: Cyber-physical System Adaptation in One Control Problem for Supply Chain
**

**Inna Trofimova, Boris Sokolov, Dmitry Nazarov
**

In this paper, it is provided to discuss
the supply chain optimization problem in the event of unexpected circumstances happen and the
relevant data about the actual system state (delivery status, preserving temperature, actual stock, availability of transport facilities, etc.) could be timely obtained. To optimize the receiving process of current information the scheduling problem of retrieving and handling information is considered. To describe supply chains operation and optimize it we use the dynamic systems with control and design optimal program and position controls.
The advance of this
paper is that cyber-physical system has been applied in the SC optimization problem when it is essential to do real-time reaction when unexpected circumstances happen for
improving the timeliness of the
relevant data about the actual supply chain state. We combine considered models and apply classical control theory methods
for solving this supply chain management problem.

**
ID 054: National Healthcare System and Economy's Competitiveness
**

**
Anatoliy Sigal, Maria Bakumenko, Elena Lukyanova
**

In the paper, the authors test the hypothesis about the correlation of ranks between a country's
healthcare system and the national competitiveness. The research rests upon data that are given in reports
by the World Health Organization, the World Economic Forum and the consulting firm Bloomberg.
The authors measure the statistical relationship between the examined couples of order variables with the help of Kendall's
coefficient of concordance and assess the statistical significance of a sample value of the concordance coefficient using Pearson's
chi-square test. The found sample values of the concordance coefficient are rather close to 1, so there is a strong correlation of
ranks between the examined couples of order variables. The conclusion can be made that the level of a country's healthcare
system has a strong impact on the national competitiveness.

**
ID 061: Assessment of the Socio-Economic Effectiveness of Innovative Projects
**

**
Elena Lezhnina, Yulia Balykina, Alexander V. Konovalov
**

In the decision-making process on the construction of large-scale projects, it is necessary to take into account not only the economic benefits for investors, but also the possible long-term socio-economic impact on the region. Moreover, this influence is both positive and negative. To carry out such an assessment, it is necessary to determine the financial indicators of the project, as well as the factors of possible impact on the social life of the region, and environmental impact. This article addresses the issue of using migrant labor. Its positive and negative socio-economic impact on the region is explained.

**ID 210: Dynamic Input-Output Models: Analysis of Possibilities and Trends Control
**

**Nikolay Smirnov, Viktor Peresada, Kirill Postnov, Tatiana Smirnova, Yefim Zholobov
**

The Input-Output (IO) models proposed by Leontief are an effective tool for scientific modeling of various economic processes. At the same time, dynamic IO models are of particular importance. They are used to analyze macroeconomic trends. The authors of this work are confident that the theoretical and applied results of modern mathematical control theory can be effectively used in dynamic IO models. It is shown that the process of implementing investment programs is equivalent to the problem of constructing program controls, and their corrections in the presence of some disturbances can be modeled as problems of synthesis of stabilizing feedbacks. Moreover, the notions of an investment scenario and a group of acceptable scenarios are introduced. In the framework of the proposed model, the problem of choosing the structure of the control system is discussed. The results of numerical experiments are presented. In conclusion, the problem of multi-program control is formulated.

#### On the Strong Time-Consistency of Set-Valued Optimality Principles

##### Leon Petrosyan

In the paper, the evolution of dynamic game along the cooperative trajectory is investigated. The following problem connected with this evolution is considered: under what conditions the initial optimal solution converted to any optimal solution in the subgame with initial conditions on the cooperative trajectory, will remain optimal in the initial game. We call it strongly time consistency. If this condition is not satisfied, players in some time instant in the current subgame may switch from the previously selected optimal solution to any optimal solution of this subgame and as result realize the solution which will be not optimal in the whole game. We propose different types of strongly time-consistent solutions for cooperative differential and dynamic games.

#### Systems with Propagation: A Bunch of Models and a Research Programme

##### Vladimir Rasvan

There are discussed here several applications of Physics and Engineering which are described by 1D propagation - hyperbolic partial differential equations in two dimensions (time and one space dimension for distributed parameters) having nonlinear and nonstandard boundary conditions. Nonstandard boundary conditions means they contain ordinary differential equations. It is presented the association of a system of functional differential equations and the one to one correspondence between the solutions of the two mathematical objects. In most cases the functional differential equations thus associated are of neutral type having (sometimes) a marginally stable difference operator. A set of open problems for these equations is listed.

#### Stability, Part 2

##### Session WeA1. Chairs: Alexander Aleksandrov, Alexey Platonov

Location: Zoom ID: 989 8334 3245, https://youtu.be/OJ9QE1KjtLk

**ID 203: Stability of Weak Solutions of Parabolic Systems with Distributed Parameters in a Network-Like Domain
**

**
Alexey Zhabko, Vyacheslav Provotorov
**

The paper considers the behavior of the solution of the evolutionary parabolic equation with unlimited increase of the time variable. The paper uses the classical understanding of the stability of the solution of a differential equation or a system of equations that goes back to the works of A.M. Lyapunov: a solution is stable if it little changes under the small perturbations of the initial condition. In the work specified the stability conditions for the solution of an evolutionary parabolic system with distributed parameters on the net-like domain describing the process of transfer of a continuous medium in a space network are indicated (this takes on particular importance when studying the dynamics of multiphase media). The obtained results underlie the analysis of optimal control problems for differential systems with distributed parameters on a graph, which have interesting analogies with multiphase problems of multidimensional hydrodynamics.

**ID 171: Mixed Feedback Feedforward Frequency Control in Power Systems
**

**
Oleg Khamisov
**

The presented work addresses one of control aspects of power systems: frequency control. In contrast to other transportation networks, here it is not possible to store electrical energy in amounts sufficiently large for reliable system operation. As a result, generation must always be equal to the demand and frequency oscillations are indicator of power imbalance. New proportional-integral controller is derived in order to provide fast response in both feedback and feedforward modes. Linear power system model is analyzed. Second-order turbine governor dynamics is considered in order to ensure high quality of the model. Proof of global asymptotic stability is given. Faster frequency stabilization in comparison with the existing frequency control is shown by numerical simulations.

**ID 118: Minimax Approach in a Multiple Criteria Stabilization of Singularly Perturbed Control
**

**Stanislav Myshkov, Vladimir Karelin, Lyudmila Polyakova
**

The multiple criteria linear-quadratic control problem
for
singular perturbed systems is considered.
The case when only
dominant states in the output feedback are used
is discussed. It
is known that the lack of information about all
states does not
permit to design a control which minimizes the
quadratic
functional for arbitrary initial states.
There are several
modifications of the problem that permit
to escape that factor.
For non-stationary case, the multiple
criteria linear-quadratic
control problem has been considered
in [7]. In the paper,
the minimax approach is discussed
for stationary case and thereby
the discrete minimax problem is solved.
The presence of regular
and singular perturbations in the dynamics
is the main difference
between this paper and the previous works.

**ID 207: Polynomial Stabilizability and Homogeneity
**

**Chaker Jammazi, Mohamed Boutayeb
**

In this paper, the problem of polynomial stabilization of control systems is presented with the homogenous approximation. Homogeneous feedbacks stabilizing polynomially some key systems, as well as the harmonic oscillator, the angular momentum and the Brockett's integrator are built.

#### Game Theory. Conflict Systems Control, Part 1

##### Session WeB1. Chairs: Elena Parilina, Ekaterina Gromova

Location: Zoom ID: 914 5699 7454, https://youtu.be/oPDHCtiBWTQ

**ID 186: On Nash Equilibrium in Repeated Hierarchical Games
**

**
Yaroslavna Pankratova, Leon Petrosyan
**

In this paper, we investigate repeated hierarchical games and the cooperative version of these games. As a solution concept in the repeated hierarchical game, we consider Nash Equilibrium. Moreover, a set of different Nash equilibrium, based on threat and punishment strategies, is obtained. Additionally, we compute the Price of Anarchy (PoA) and the Price of Stability (PoS)

**ID 039: A Pollution Control Problem for the Aluminum Production in Eastern Siberia: Differential Game Approach
**

**
Ekaterina Gromova, Anna V. Tur, Polina Barsuk
**

In this paper, we apply a dynamic game-theoretic model and analyze the problem of pollution control in Eastern Siberia region of Russia. When carrying out the analysis we use real numerical values of parameters. It is shown that
cooperation between the major pollutants can be beneficial not only for the nature but also for the respective companies.

**ID 196: Dynamic Shapley Value for 2-Stage Cost Sharing Game
**

**Yin Li
**

The problem of constructing the Dynamic Shapley values in a two stage game is studied. During the dynamic game, each stage game can be considered as a minimum cost spanning tree game. From the first stage, the players’ strategy profiles construct the graph in stage games, and the minimum cost spanning tree of the graph is defined by Prim (1957). At the second stage, the graph built by the players will be changed in some possible ways, with several specified probabilities. These probabilities are determined by the strategy profiles of players in the first stage. The meaning of the change is to break several edges on the graph. Then the players’ cooperative behavior is defined. Along the cooperative trajectory, characteristic functions are defined for all coalitions. The IDP(Imputation Distribution Procedure) was used to construct Dynamic Shapley Values.

**ID 043: Dynamic Programming Equations for the Game-Theoretical Problem with Random Initial Time
**

**Anastasiya Malakhova, Ekaterina Gromova
**

A class of differential games with random initial time is considered. It is shown that payoff function in such class of games can be simplified to the form suitable for using of standard dynamic programming approach for both, the competitive and cooperative schemes. In order to find the Nash Equilibrium a form of the Hamilton-Jacobi-Bellman equation is obtained.

#### Dynamic Systems Theory, Part 1

##### Session WeA2. Chairs:Alexander Kamachkin, Dmitriy Potapov

Location: Zoom ID: 989 8334 3245, https://youtu.be/OJ9QE1KjtLk

**ID 058: To Identification of Integral Models of Nonlinear Multi-Input Dynamic Systems Using the Product Integration Method
**

**
Svetlana Solodusha
**

This paper focuses on a method for identifying Volterra polynomials in the case of a vector input signal. The key idea behind the new approach to constructing integral polynomials is based on the identification of integrals from Volterra kernels. Based on a generalization of the product integration method (pi-method), an algorithm for the numerical reconstruction of the cubic Volterra polynomial in the vector case is proposed. A significant distinctive feature of this approach, based on the use of pi-approximations of multidimensional convolutions, is the problem reduction to solving some system of linear algebraic equations (SLAE) instead of solving multidimensional Volterra integral equations of the first kind. The practical part of the paper addresses the application of Volterra polynomials in the problem of modeling the nonlinear dynamics of a heat exchanger element. The results of the computational experiment showed that the new approach in most cases increases the accuracy of modeling.

**ID 033: Optimal Damping Problem for Diffusion-Wave Equation
**

**
Sergey Postnov
**

In this paper we consider a model system, which defined by a one-dimensional
non-homogeneous diffusion-wave equation. For such system we investigate an optimal damping problem as optimal
control problem of the following type: we need to transfer the system from given initial state to the final
state with zero time derivative of system state. Two types of optimality analyzed: control norm minimization at given control time
and time-optimal control search at given restriction on control norm. In general case we consider both of boundary and distributed
controls which are $p$-integrable functions (including p=infty). We use an explicit solution for diffusion-wave equation in order
to reduce the optimal control problem to an infinite-dimensional l-problem of moments. We also derived the finite-dimensional l-problem
of moments using an approximate solution of the diffusion-wave equation. For this problem the correctness and solvability are analyzed.

**ID 187: Algorithmization of Receiving Orbits of Weierstrass and Orbits of Tangences
**

**Maria Shagai, Maikl Iofe, Aleksandr Flegontov
**

This article analyzes families of equations such as the Weierstrass orbit, the tangent orbit solutions of which have a special structure. The relations are derived for these classes, on the basis of these relations (according to a finite set of functions) solutions are constructed for some generalized homogeneous Emden-Fowler equations through a finite set of special functions. This is done for algorithmizing the process of searching for new equations. Such interpretation of equations will be useful to specialists in the field of differential equations

**ID 109: Algorithm for Constructing a Cognitive Aggregate-Stream Model of the Automatic Spacecraft Flight Control Process
**

**Boris Sokolov, Vladimir Kovtun, Valerii Zakharov
**

The resource consumption of onboard systems (OS) largely depends on the synergetic phenomena that occur during intersystem interaction in automatic spacecraft (AS). By using these phenomena, it is possible to increase the efficiency of using existing resources, as well as to supplement them with new ”synergistic” resources [3]. At the same time, synergetic phenomena can lead to premature development of the OS resource and unforeseen (non-calculated) failures and accidents [2]. For a targeted search for data on synergetic phenomena, special modeling of processes occurring on board is required. The purpose of the research was to move from the system-cybernetic model of the AS as a ”black box ”to a model that provides” transparency ”of the AS as a” white box” for processes occurring on board [6], taking into account synergetic phenomena. A new algorithm for constructing a cognitive aggregate-flow model of the AS flight control process is considered.

#### Game Theory. Conflict Systems Control, Part 2

##### Session WeB2. Chairs: Elena Parilina, Ekaterina Gromova

Location: Zoom ID: 914 5699 7454, https://youtu.be/oPDHCtiBWTQ

**ID 032: Minimal Current Payments Algorithm for Sustainable Cooperation in Multicriteria Game
**

**
Denis Kuzyutin, Yaroslavna Pankratova, Roman Svetlov
**

To ensure sustainable cooperation in a dynamic game we adopt the so-called imputation distribution procedure (IDP) based approach.
A novel IDP which satisfies time consistency, irrational-behavior-proof property and "reward immediately after the move"
assumption is designed for multistage multicriteria games with perfect information. This payment schedule implies the minimal
current non-negative payments to the players along the optimal cooperative path.

**ID 035: Pursuit of Rigidly Coordinated Evaders in a Linear Problem with Fractional Derivatives, a Simple Matrix and Phase Restrictions
**

**
Alyona Machtakova, Nikolai Petrov
**

This paper addresses the problem of catching at least one evader under the condition that the motion of all participants is described by a linear system with fractional derivatives and a simple matrix and that all evaders use the same control and do not move out of a convex cone. The terminal sets are the origins of coordinates.
Sufficient conditions for capture are obtained in terms of the initial positions and parameters of the game.

**ID 064: Differential and Algebraical Relations in Singular Sets Construction for a One Class of Time-Optimal Control Problems
**

**Aleksandr Uspenskii, Pavel Lebedev
**

We consider the Dirichlet boundary value problem for the Hamilton-Jacobi equation, the minimax solution of which coincides with the optimal result function for one class of time-optimal control problems. The approach to constructing a solution to a boundary value problem applied in this article is based on identifying the conditions for the appearance of a singularity of a solution depending on the geometry of the boundary set and the differential properties of its boundary. The effectiveness of the developed theoretical methods and numerical procedures is illustrated with an example.

**ID 078: Subgame Perfect Pareto Equilibria for Multicriteria Game with Chance Moves
**

**Denis Kuzyutin, Nadezhda Smirnova, Igor Tantlevskij
**

For n-person multicriteria extensive-form game with chance moves we prove the existence of pure strategy subgame perfect Pareto equilibrium (SPPE). Then using the minimal sum of relative deviations approach we specify the method for choosing a unique SPPE.

#### Dynamic Systems Theory, Part 2

##### Session WeA3. Chairs:Alexander Kamachkin, Dmitriy Potapov

Location: Zoom ID: 989 8334 3245, https://youtu.be/OJ9QE1KjtLk

**ID 204: Normalizing Random Vector Anisotropy Magnitude
**

**Kirill Chernyshov
**

In the context of the anisotropic control theory (Anisotropy of Signals and the Entropy of Linear Stationary Systems / I.G. Vladimirov, A.P. Kurdjukov, A.V. Semyonov: Doklady Math., 1995, vol. 51, pp. 388-390), vanishing the system α-anisotropic norm corresponds with H2-theory, while its going to infinity, with H∞-theory. Meanwhile, this definition considerably involves just the magnitude of α, the mean random vectors sequence anisotropy that characterizes the uncertainty degree. Thus, proper selection the random vector anisotropy magnitude to determine the system α-anisotropic norm is of importance. Accordingly, the paper presents an approach to constructing a normalization procedure of the anisotropy magnitude as a mapping of the positive semiaxis in the unit interval.

**ID 019: Synchronization in Feedback Cyclic Structures of Oscillators with Hysteresis
**

**
Alexander Kamachkin, Dmitriy Potapov, Victoria Yevstafyeva
**

We study synchronous processes in a complex system with cyclic links. The system represents some hysteresis-feedback oscillators coupled in a ring. Besides, each oscillator has an additional feedback with the next oscillator. We establish sufficient conditions for the existence of the periodic or recurrent motions of the system. The periodic motion corresponds to a synchronous process in the system. We obtain conditions for synchronization to arise and also conditions for the stability of synchronous oscillatory processes in two special cases.

**ID 112: A Method of Determining of Switching Instants for Discrete-Time Control Systems
**

**Sergey Khryashchev
**

In this paper, dynamical polysystems with piecewise constant controls are considered.
Provided that the dynamical system is controllable in continuous time, the question of its controllability in discrete time is also studied.
Controls in discrete time are constructed by using the theory of multidimensional continued fractions.
Discrete switching instants found using continued fractions approximate continuous switching instants.

#### Game Theory. Conflict Systems Control, Part 3

##### Session WeB3. Chairs: Elena Parilina, Ekaterina Gromova

Location: Zoom ID: 914 5699 7454, https://youtu.be/oPDHCtiBWTQ

**ID 045: Two Echelon Supply Chain: Market Search Behavior and Dependent Demands
**

**
Suriya Kumacheva, Victor Zakharov
**

Nowadays supply chain management (SCM) is one of the most popular and intensively developed areas of applied mathematics. The necessity of studying and modelling the processes of interaction between the manufacturer, suppliers and final purchasers of products requires such mathematical tools as game theory and applied statistics.
Like many earlier works, the presented paper considers a model of the supply chain with one manufacturer and two retailers. The game-theoretical approach is applied to design and study two echelon supply chain model with market
search behavior and dependent demands of customers. At the same time retailers play Cournot game. Retailers'
demands supposed to be mutually dependent random variables which joint distribution is assumed to be known.
Constructive method to find Nash Equilibrium in pure strategies for two echelon supply chain model with market
search behavior of retailers and dependent demands of customers is proposed.

**ID 014: DEA Modeling with Cluster Analysis
**

**
Vladimir Bure, Elena Parilina, Kseniya Staroverova
**

We present a model of clustering the homogeneous firms using the numerical characteristics representing efficiency of their activities during a given time interval. The firm's efficiency is found by the DEA (Data envelopment analysis) methodology, which is based on solving several optimization problems. The DEA modeling gives an opportunity to compare firms' efficiencies taking into account several factors of their activities. The second step of the analysis we make is to define the partition of the time series showing the firms' efficiencies. We find the clusters of firms close to each other in some sense. We also propose the method of finding a stable partition of firms according to their efficiencies.

**ID 028: Cooperation in Vehicle Routing Game on a Megapolis Network
**

**Alexander Mugayskikh
**

In this work cooperative multiple depot open vehicle routing problem (MDOVRP) is considered. The underlying model is a time-dependent variant of classic VRP which presents congested traffic in a megapolis more correctly compare to its nontemporal flavor. With the aim to reduce operational expenses on transportation costs or rent for the vehicles, carrier companies can share the customers with each other by forming coalitions. We introduce Direct Coalition Induction Algorithm (DCIA) for constructing the characteristic function of TD-MDOPVR game that satisfies subadditive property. Shapley values calculated for the problem in- stance of 150 customers and 3 companies are compared with costs before cooperation. All numerical runs are performed on a graph of real road network of Saint-Petersburg which includes 255 nodes and 1251 arcs. Time-dependent travel times are obtained by solving traffic assignment problem in case of Wardrop’s user equilibrium.

#### Medical and Biological Systems Control, Part 1

##### Session ThA1. Chairs: Gerasim Krivovichev

Location: Zoom ID: 986 9422 1539, https://youtu.be/MWAJ-3plXWI

**ID 042: Some Problems of Modeling the Human Body Subjected to Vertical Vibration
**

**
Vladimir Tregubov, Nadezhda Egorova
**

The problem of determining the structure and parameters of a mechanical model of a human body subjected to vibration is analyzed.
This is extremely important for using this model to construct a vibration protection system. Based on the example of a
two-mass mechanical model of a human body it was found that to determine the model structure and its parameters, it is necessary to know
the total model mass and the amplitude-frequency response (AFR) for both solids in the model structure. An alternative is to have an input mechanical impedance (IMI) and to know the mass of one of the solids in the model structure. In addition, using mechanical models with an arbitrary number of degrees of freedom, the influence of multi-articular muscles on the frequency characteristics of a human body was found out. The possibility of additional antiresonance frequencies and their presence in the
upper mass is shown.

** ID 106: Clusterization of White Blood Cells on the Modified UPGMC Method
**

**Andrey Orekhov, Victor Shishkin, Nikolay S. Lyudkevich
**

Modern methods of flow cytometry make it possible to characterize cell populations with unprecedented detail, but the traditional analysis of data using the ``manual gating'' method under these conditions is ineffective and unreliable. In recent years, a large number of research papers have been published that describe specialized clustering algorithms for detecting and determining populations of white blood cells. However, problems related to the presence of noise and different data density remain relevant. The internal problem of cluster analysis associated with determining the preferred number of clusters, and the moment the process itself stops remains unresolved. It is proposed to use the modified UPGMC method with the Markov moment of stopping the clustering process from eliminating noise and overcoming problems associated with different data density.

**
ID 083: HIV Incidence in Russia, Ukraine and Belarus. SIR Epidemic Analysis
**

**
Sergei Sokolov, Alexandra Sokolova
**

The problem of predicting the incidence rate of the human immunodeficiency virus (HIV) in Russia, Ukraine and Belarus is considered. The official morbidity levels as initial data for numerical modelling are taken. The search for the coefficients of the model is examined in detail using gradient descent with an auxiliary system applied. The $R_0$ value is calculated. The incidence of HIV in Russia, Ukraine and Belarus is compared and the difference is discussed.

**
ID 175: Elasticity's Influence on Biomechanical Model of Corneoscleral Shell Under Vacuum Compression Ring
**

**
Dmitry Franus
**

The research deals with biomechanical model for the stress-strain state of the corneoscleral shell of the human eye under loading by a vacuum compression ring. A three-dimensional finite-element model of the contact problem of loading of the multilayer isotropic corneoscleral shell of variable thickness is presented. Influence of such parameters as sclera elasticity, corneal stroma elasticity, vacuum level, corneal thickness, and length of longitudinal axis of the eyeball on the value of IOP is studied.

#### Mathematical Modeling and Image Processing Methods, Part 1

##### Session ThB1. Chairs: Elena Kotina, Aleksandr Krivoshein

Location: Zoom ID: 914 3601 2104, https://youtu.be/SgW_EcYGOiQ

**
ID 048: Computation and Analysis of Two-Phase Filtration Using Averaged Models in Oil Formations with Both Vertically Stratified Heterogeneity and Horizontal Zonal Heterogeneity
**

**Sergei Plokhotnikov, Dilbar Bikmukhametova, Kuan Ming Tho, Svetlana Enikeeva
**

The paper considers averaged models of two-phase filtration in oil formations with both vertically stratified heterogeneity and horizontal zonal heterogeneity. Comparative analysis of numerical solutions of averaged two-dimensional models, with modified relative phase permeability and laboratory phase permeability, and solutions of a three-dimensional model was carried out.

**
ID 111: Automatic Recognition of Metal Smelting Quality Using Machine Vision
**

**Mikhail Shirobokov, Valery Grishkin, Artemii Grigorev
**

The paper proposes a prototype of a computer vision based algorithm, which allows automatic quality control of one of the intermediate stages of metal smelting at a steelworks. During the transfusion of molten metal, the algorithm works with the data obtained from IP camera and makes it possible to determine deviations from the norm of the quality parameters of smelting from a real-time video stream. The algorithm consists of two stages. At the first stage, every frame is checked for containing the process of transfusion of molten metal. If the process is registered, at the second stage the frame is processed in order to calculate metrics that allow to estimate the amount of molten metal or bright fire in it, as well as the presence and amount of dim flame and smoke. If the metric values exceed thresholds, the operator receives a warning about possible problems and takes appropriate action.

**
ID 176: An Alternative Approach to Managing the Nitrogen Content of Cereal Crops
**

**
Vladimir Bure, Olga Mitrofanova
**

Fertilizers are actively used in agriculture, and nitrogen is a main introduced agrochemical for cereal crops. It’s necessary to study crops nitrogen status managing approaches by determining reasonable doses of fertilizer applied. The crop production process dynamic modeling method is difficult to apply in practice, as its implementation requires obtaining a large number of initial parameters. In this connection, an alternative approach to control the crops nitrogen content based on the remote sensing processing is proposed. Cereal crops aerial photographs are used as the initial data of the problem under consideration. In addition, ground-based measurements can be used. Two approaches to solve this problem based on image processing are proposed: classification with a training data, spatial interpolation using geostatistical methods.

**ID 099: Optimization Method of the Velocity Field Determination for Tomographic Images
**

**
Elena Kotina, Pavel Bazhanov, Dmitry Ovsyannikov
**

The digital image processing problem basing on velocity field determination is considered. An optimization method for constructing the velocity field basing on the study of the integral functional on the ensemble of trajectories is developed. The analytical form of functional variation allows using directed optimization methods to find the desired parameters. This method is considered for 3D tomographic image processing, in particular for PET images for the movement correction in dynamic studies.

#### Optimization Methods, Part 1

##### Session ThA2. Chairs: Vladimir Noghin, Alexander Krylatov

Location: Zoom ID: 986 9422 1539, https://youtu.be/MWAJ-3plXWI

**ID 067: Methodology of Structural-Functional Synthesis for the Small Spacecraft Onboard System Appearance
**

**
Valerii Zakharov, Alexander Pavlov, Valentin Vorotyagin, Dmitry Pavlov
**

To increase the degree of validity of design decisions when creating a small spacecraft, a methodological approach is proposed for the structural-functional synthesis of the appearance of its onboard systems. The proposed approach allows to perform multi-criteria selection of effective configuration variants for onboard system of a small spacecraft, taking into account various types of structural reservation of onboard equipment, a wide assortment of element base. The conceptual and mathematical formulations of the problem of structural and functional synthesis of the appearance of the onboard system of a small spacecraft are presented. An algorithm has been developed for multicriteria synthesis of the appearance of the onboard system of a small spacecraft, which is based on the interval lexicographic method for removing criterial uncertainty.

**
ID 016: A New Characterization of Cone Proper Efficient Points
**

**
Vladimir Noghin
**

The paper deals with a vector optimization problem in which the outcome space is partially ordered by some cone relation. A cone proper efficiency which was introduced by M.I. Henig is considered as the main optimality notion. Instead of Henig's characterization of vector optimization problem using weighted sum of criteria we present a new characterization of cone proper efficient points in terms of goal programming, i.e., by minimizing the distance between the outcome set and some totally dominating point.

**
ID 055: Particular Structures of the Pareto Set and Its Reduction in Bi-criteria Discrete Problems
**

**
Aleksey Zakharov, Yulia Kovalenko
**

Bi-criteria discrete problems are analyzed in the context of the Pareto set reduction approach proposed by V. Noghin. We construct families of the instances with special structures of the Pareto set and theoretically analyze the reduction. Practical application of the results is presented for the bi-criteria set covering problem.

** ID 179: A Computational Approach to Estimating Activity Coefficients Using Gibbs Energy Minimization
**

**Roman Voronov, Anton Shabaev, Fedor Vasilyev
**
Systems that are of interest in thermodynamic modeling for industrial applications contain solution phases, which are not ideal mixtures. To account for deviations from ideal behavior in a mixture of chemical substances, activity coefficients are used. They can be determined experimentally by making measurements of non-ideal mixtures: theoretical laws provide a value for an ideal mixture, against which the experimental value is compared to obtain the activity coefficient. The research novelty is the computational procedure for estimating missing activity coefficients assuming that the system is in equilibrium state, and some activity coefficients are known, which in a sense is the inverse problem to Gibbs energy minimization. The proposed computational procedure allows the mathematical evaluation of some missing activity coefficients instead of running an experiment, which constitutes its main practical contribution.

#### Artificial Intelligence, Part 1

##### Session ThB2. Chairs: Ivan Blekanov

Location: Zoom ID: 914 3601 2104, https://youtu.be/SgW_EcYGOiQ

**ID 129: Multilingual Sentiment Analysis for User Discussions on Social Networks: An Approach Based on a Modified SVM Algorithm
**

**
Mikhail Kukarkin, Ivan Blekanov
**

Sentiment analysis of users' messages on social networks is a compelling task in terms of both academic research and application of the research results to real-world business analytics. One of the key problems of sentiment detection in real-world discussions on social media is their mixed languages and, thus, the demand for multilingual instruments. In this paper, we, first, shortly describe the existing research on multilingual sentiment analysis. We suggest our own approach of data processing for classification and an enhanced sentiment detection method based on the SVM algorithm. To evaluate these methods, we apply them to marked-up noisy data from ad hoc discussions on social networks (in English, Russian, French, and German language) and clean data from Twitter US Airline Sentiment collection and assess the quality of sentiment detection by standard metrics. We show that our method reaches highest values of F1-score (0.78 and 0.94) for noisy and clean datasets.

**
ID 126: On the Possibility of Using Neural Networks for the Specific Problems of Meteorological Forecasting
**

**
Irina Tokareva, Elena Stankova
**

The paper explores the possibility of forecasting such dangerous meteo-rological phenomena as a thunderstorm by applying a neural network to the out-put data of a hydrodynamic model that simulates dynamic and microphysical pro-cesses in convective clouds. The presented work continues the studies described in [3, 4, 5, 6, 7]. The results show that the use the proposed approach allows us to achieve a forecast accuracy of 91.6%.

**
ID 185: Metric for Comparison of Graph-Theoretic Models of the Same Dimension with Ordered Vertices
**

**
Nikolai Moskin
**

The work is dedicated to methods of comparison and classification of graph-theoretic models which are known within the direction of graph matching. It contains an overview of metrics for comparing graphs based on a maximum common subgraph. A modification of the measure based on a maximum common subgraph is proposed, which takes into account the ordering of vertices (each vertex is associated with its unique serial number). If the graphs have the same dimension (i.e. same number of vertices) it is shown that this measure satisfies all the properties of the metric (nonnegativity, identity, symmetry, triangle inequality). It is assumed that this metric can be used to solve the problem of text attribution.

** ID 077: Topic Models with Neural Variational Inference for Discussion Analysis in Social Networks
**

**Nikita Tarasov, Ivan Blekanov, Alexey Maksimov
**Topic models and their extensions are widely used to represent documents using generative probabilistic models. Many models were developed and applied to analyse the content of news articles, scientific papers and other sources of textual data. However these classic algorithms have severe problems when dealing with short texts, processing multilingual and noisy data. These problems are most prevalent in the task of analysing corpora collected from social networks. Authors consider different topic models for users’ discussion analysis in social networks. Authors evaluate topic modelling results of these approaches using a modified NPMI measure. The standard news20 dataset was used as a test collection as well as two user discussions on Twitter in both Russian and English. The experiment showed that a combination of ETM and pretrained embeddings based on ELMO, vastly outperforms traditional topic models such as BTM while analysing short and unbalanced texts such as Twitter messages.

#### Optimization Methods, Part 2

##### Session ThA3. Chairs: Lyudmila Polyakova, Majid Abbasov

Location: Zoom ID: 986 9422 1539, https://youtu.be/MWAJ-3plXWI

**ID 062: On a Support Function on a Convex Cone
**

**
Lyudmila Polyakova, Alexander Fominyh, Vladimir Karelin, Stanislav Myshkov
**

The concept of the support function of a convex set is one of the key
in convex analysis.
It was introduced by German mathematician
H. Minkowski in the late 19th century.
In this paper the properties
of support functions on a closed
convex cone are considered.
For a convex compact set the concept of a forming
set with respect
to this cone is introduced.
The properties of this set are studied.
The forming set is important as it allows
to calculate the value of
the support function on this cone without information
about all
the elements of the considered set.
Conditions under which support
functions of the two sets on the cone are equal
are derived. Some drawings illustrate these properties.

**
ID 105: The Sensitivity of Traffic Flow Re-assignment Process in Network Optimization Problems
**

**
Anastasiya Raevskaya
**

Traffic assignment models and methods are under consideration of researchers all around the world. The development of this scientific field contributes both in theory and practice. In this paper, the traffic re-assignment procedure is analyzed from sensitive perspectives. This procedure is given in the form of computational techniques to cope with the network optimization problem. Numerical experiments are performed for several types of travel time functions. The results reveal that, from practical perspectives, dual algorithms are highly sensitive to parameters of travel time functions, while primal algorithms can be quite acceptable for rough computations. The obtained findings contribute to the theory and give fresh managerial insights for traffic engineers.

**
ID 031: On Degree of Pareto Set Reduction Using Information Quanta
**

**
Oleg Baskov
**

The axiomatic approach to Pareto set reduction is considered. Possibility of reducing the set of possible choices to a single optimal choice is investigated. A necessary and sufficient condition of existence of a set of information quanta that allow to reduce the Pareto set to a single solution is obtained.

** ID 013: Spatial Market Equilibrium Under Linear Transaction Costs
**

**Alexander Krylatov, Yulia Lonyagina, Ruslan Golubev
**In this paper, we study the spatial market equilibrium in the case of linear transaction costs. The problem is formulated in a form of nonlinear optimization program with dual variables reflecting supply and demand prices. The unique equilibrium commodity assignment pattern is obtained explicitly via equilibrium prices. Moreover, it is proved that in order to obtain absolute values of equilibrium prices the market moderator has to establish the basic market price. Therefore, once the basic market price is given, then other prices are adjusted according to spatial market equilibrium.

** ID 085: Equivalence of Two Optimality Conditions for Polyhedral Functions
**

**
Majid Abbasov
**

In the paper we study two different optimality conditions for polyhedral functions. First one follows from the optimality conditions in terms of coexhausters, which are families of convex compact sets, that allow one to approximate the increment of the studied function at a considered point in the form of minmax or maxmin of affine functions. Second one is obtained in one of the recent publications, and is used as a core result for constructing a new optimization algorithm for finding a minimum of a piecewise affine function. Piecewise affine functions are important objects for different areas of research while coexhausters are effective for the study of a wide class of
nonsmooth functions. That is why it is important to show a connection between these two types of conditions and prove their equivalence.
This is the main aim of the present paper.

#### Artificial Intelligence, Part 2

##### Session ThB3. Chairs: Ivan Blekanov

Location: Zoom ID: 914 3601 2104, https://youtu.be/SgW_EcYGOiQ

**ID 130: Data Crawling Approaches for User Discussion Analysis on Web 2.0 Platforms
**

**
Dmitry Nepiyushchikh, Ivan Blekanov
**

This article discusses approaches to collecting data from Web 2.0 platforms such as social networks and messengers. The authors propose the implementation of a flexible architecture for a focused web-crawler to collect data of users discussion in the social network Facebook and the Telegram messenger. The proposed crawler is based on interaction with a platform's API, get/post requests and simulating actions in a browser. The authors set up an experiment comparing implementation of proposed data crawling approaches. The data on the COVID-19 virus was collected from Facebook social network and Telegram messenger using RUM Extractor for Facebook and large number open source Telegram crawles. Developed focused crawler reached the speed of 15 participants per second and 12 posts per second without blocking account when processing a user discussion in Facebook. Telegram crawles showed the speed of 200 participants per second and 300 posts per second without blocking.

**
ID 075: Characteristics of Lexical Spectra of Texts in the Problem of Establishing Authorship
**

**
Nikolai Moskin, Kirill Kulakov, Alexander Rogov, Roman Abramov
**

The lexical spectrum is a significant characteristic for solving the problem of determining the authorship of texts (for example, when solving the problem of attribution of texts that may belong to F. M. Dostoevsky). However, the application of some data mining methods (for example, decision trees) requires representing the spectrum as a single number that would adequately reflect its structure. We consider the approximation of lexical spectra (at the dictionary level and at the text level) by hyperbolic and exponential curves. Based on the articles from the pre-revolutionary journal "Time" (1861-1863), it is shown that the coefficients of hyperbolic regression approximate the data much better than the coefficients of the exponential curve. In this case, the chi-squared distance was used to determine the difference between the spectra. The research was carried out using the SMALT information system, where automated marking of works was implemented with manual control of specialists-philologists.

**
ID 181: Research of Features of Dostoevsky's Publicistic Style by Using N-grams Based on the Materials of the "Time" and "Epoch" Magazines
**

**
Roman Abramov, Kirill Kulakov, Alexander Lebedev, Nikolai Moskin, Alexander Rogov
**

The paper is devoted to the study of the publicistic style of F. M. Dostoevsky on the basis of publications in the journals "Time" and "Epoch" (1861-1865). For this, fragments of texts (including other authors: M. M. Dostoevsky, N. N. Strakhov, A. A. Golovachev, etc.) were selected in sizes of 500, 700 and 1000 words, on which the occurrence of bigrams and trigrams (encoded sequences of parts of speech) were counted. Decision trees were built on their basis and an analysis of the accuracy of text recognition was performed. If we consider the classification at the first level of the tree (fragment size 1000), then the accuracy was on average 87%. This feature is the percentage of the presence of the "adjective-noun" bigram. When analyzing trigrams, the most significant feature at the first level was the "noun-adjective-noun" sequence. The article also discusses the problem of comparing the resulting decision trees.

#### Round table dedicated to the memory of V. I. Zubov

"A Person and a Scientist"

##### Session RT1. Chairs: Leon Petrosyan, Nikolay Smirnov

We invite everyone who can share their memories and those who are interested in listening to them. Time limit is 3 - 5 min. for a short note.

#### Medical and Biological Systems Control, Part 2

##### Session FrA1. Chair: Gerasim Krivovichev

Location: Zoom ID: 922 5024 6030, https://youtu.be/7FxAmqeTntU

**ID 072: Detection of the Community-Acquired Pneumonia Factors Leading to Death
**

**
Alexandra Arzhanik, Anastasia Goncharova, Daria Vinokurova, Evgeny Kulikov
**

The aim of the paper was to detect the factors leading to the death of patients classified as light on the CURB-65 scale. We performed a retrospective analysis of 1412 case histories of hospitalized community-acquired pneumonia patients in all hospitals in the Tomsk Region in 2017. All patients were categorized into different groups based on lethality and CURB-65 score. We analyzed age, gender and laboratory indicators. Significant indicators of an adverse outcome were identified. It is necessary to modify the scale and take into account a larger number of indicators.

** ID 023: One-Dimensional Non-Newtonian Models of Arterial Hemodynamics
**

**Gerasim Krivovichev
**

The one-dimensional models of non-Newtonian hemodynamics are considered. The models are constructed by the averaging of 3D incompressible Navier-Stokes system on the vessel cross-section. The Power Law, Carreau-Yasuda and Cross non-Newtonian models are compared with the inviscid and Newtonian models. In dimensionless variables, it is demonstrated that the small parameter exists in the system, and the perturbation method can be applied for the solution of nonlinear problems. For the smooth initial condition, it is demonstrated that in comparison with the Newtonian model, the strongest damping of the solutions takes place for the non-Newtonian models.

**
ID 160: Comparison of the Stress-Strain State of the Human Eye After PRK, LASIK and SMILE Surgeries
**

**
Svetlana Bauer, Liudmila Venatovskaya, Andrey Kachanov, Vladimir Kornikov, Boris Zimin
**

The stress-strain state of the human eye, which cornea in its apexis is weakened after myopia surgical correction, is studied. The elastic system "cornea-sclera" is presented as two joint transversely isotropic spherical segments with tapered thickness, different radii of curvature and biomechanical properties. Cornea is modeled as multilayer shell. The simulated eye shell is loaded with internal pressure. Mathematical models of three different laser vision correction surgeries: small incision lenticule extraction (SMILE), laser in situ keratomileusis (LASIK) and photorefractive keratectomy (PRK), are developed in the engineering simulation software ANSYS Inc. The diameter and thickness of the lenticular in SMILE, the diameter of the ablation zone and the maximum thickness (depth) of the corneal ablation in LASIK and PRK define optical surgery areas and are considered as comparable parameters.

#### Mathematical Modeling and Image Processing Methods, Part 2

##### Session FrB1. Chairs: Elena Kotina, Aleksandr Krivoshein

Location: Zoom ID: 939 8906 7190, https://youtu.be/HD3xzv8WEGc

**
ID 172: Parametrization of Orthogonal Hexagonally Symmetric Low-Pass Filters
**

**Aleksandr Krivoshein
**

A complete parametrization of hexagonally symmetric orthogonal low-pass filters for the case of dyadic matrix dilation and small supports is given. Methods for the construction of high-pass filters are also discussed.

**
ID 177: Remote Sensing Data Processing for Plant Production Control
**

**Vladimir Bure, Olga Mitrofanova, Evgeny Mitrofanov, Aleksey Petrushin
**

Sustainability of agricultural production largely depends on the management of soil heterogeneity and field topography (site-specific management). Precision agriculture provides automation of such management using information technology. Remote sensing data obtaining and processing to control the plant production process using the example of aerial photography is considered. Presents the main stages of obtaining and processing aerial photographs in precision agriculture: flight plan, image processing, orthophoto generation and others. The remote sensing using seems an effective approach to solving a wide set of problems in agriculture related to monitoring the agrolandscapes state, assessing and managing their productivity.

**
ID 144: Mathematical Modeling of Cyclic Chemical Compounds
**

**
Albina Akhmetyanova, Albina Ismagilova, Fairuza Ziganshina
**

This work describes the mathematical apparatus for constructing homodesmic reactions using cyclic compounds of cis-1,2-dimethylcyclobutane and trans-1,2-dimethylcyclobutane as an example. The homodesmic method showed high reliability of the theoretical prediction of the enthalpies of formation of various compounds. The program generates a set of independent homodesmic reactions (GDR) for the test compound, which increases the reliability of the theoretical determination of the standard formation enthalpy. We have described the main stages of building a program that implements an algorithm for determining the basis of the GDR for cyclic organic compounds. For clarity of the method studied, this article provides an example of constructing a basis for homodesmic reactions, a graph and an adjacency matrix for cis-1,2-dimethylcyclobutane and trans-1,2-dimethylcyclobutane molecules.

#### Control and Optimization of Electro-Physical Processes, Part 1

##### Session FrA2. Chairs: Oleg Drivotin, Anna Golovkina

Location: Zoom ID: 922 5024 6030, https://youtu.be/7FxAmqeTntU

**ID 209: Optimization of a Real-Time Stabilization System for the MIMO Nonlinear MagLev Platform
**

**
Anna Golovkina, Sergey Zavadskiy, Mikhail Verkhoturov, Dmitri Ovsyannikov, Vladimir Kukhtin, Nicolai Shatil, Andrei Belov
**

The paper discusses optimal stabilization problem for the MagLev transport platform. The platform has a specific levitation system with four combined suspensions which include both electromagnets and permanent magnets. The presence of permanent magnets makes the problem nonlinear and incompletely controllable and causes the main challenge of this paper. In order to address it, we propose to optimize the controller with respect to the bunch of possible trajectories taking into account the mentioned nonlinearities. The controller has a dynamical structure and includes a Kalman filter with feedback on the platform gaps and electromagnet coil currents.
The introduced approach allows operating in a real-time with the presence of noise and disturbances also when platform
parameters and mass change. Optimization of stabilizing controller improves both energy costs and control accuracy.

**
ID 202: On a New Approach to RFQ Channel Optimization
**

**
Oleg Drivotin
**

The RFQ channel optimization problem is regarded as a control problem for an ensemble of dynamical systems
described by density distribution in the phase space.
Previously, for a numerical solution of this problem methods using the first variation of the trajectory were applied.
At the present work, a method based on the second variation of the trajectory is proposed. This method allows computing not only the first derivatives, but also the second ones of the quality functional over control parameters.

**
ID 104: Influence of Dyes on the Electro-Optical Properties of Liquid Crystals
**

**
Tatiana Andreeva, Marina Bedrina
**

Different molecules of liquid crystals such as 4-pentyl-4’-cyanobiphenyl (CB5), 4-(Hexyloxy)phenyl 4-butylbenzoate and their interaction with such dyes as 1,2-Diamino-4-nitrobenzene, N,N-Dimethyl-4-nitrosoaniline and dimethylamino- β-nitrostyrene were investigated by the density functional theory (DFT) using hy- brid potential method B3LYP/6-31G. The electronic absorption spectra of isolated dye molecules and the resulting complexes with liquid crystals were calculated. It was shown that the shift of the absorption bands in the spectra of the dye depends on the structure of the complex. The shift and splitting of the bands minor impu- rity dye molecules placed in the liquid crystal gives an indication of the mesophase structure.

** ID 212: Model-Based Optimal Control of Transmutation Strategy in Accelerator-Driven System
**

**Anna Golovkina, Dmitri Ovsyannikov, Ekaterina Kostina
**Optimization-based approach is developed in this paper in order to obtain the best combinations of long-lived transuranic isotopes charge to the subcritical reactor driven by accelerator. The most important isotopes were selected and nonlinear dynamic system for their concentration change is constructed. The solution of this dynamic system calculated at the end of operation time determines the radioactivity of the unloaded fuel. The goal of optimization is to reduce its total radiological impact by varying the initial nuclide densities, taking into account the physical constraints on subcriticality of reactor core. The problem is treated as nonlinear constrained programming, for which optimization algorithm based on quasi-Newton methods is suggested.

**ID 100: An Optimization Approach for Minimization of Charged Particles Orbit Deviation in Synchrotron and Transport Channels Systems Caused by Magnetic Field Tolerances
**

**Vladislav Altsybeev, Vladimir Kozynchenko
**

Optimization methods of synchrotrons and transport channels systems are considered in this report. The significant deviation of orbit of charged particles beam in this facilities causes by magnetic field tolerances. This tolerances may appeared because of deviation of real magnet length on theoretically calculated. In this report we discuss the approach of the fast channel parameter optimization technique by using swarm computations and gradient descend for improving the beam orbit. The optimizations aimed at choosing angles of correctors elements in structure of acceleration system.

#### Informatics and Control Processes, Part 1

##### Session FrB2. Chairs: Evgeny Veremey, Alina Boiko

Location: Zoom ID: 939 8906 7190, https://youtu.be/HD3xzv8WEGc

**ID 070: Multipurpose Visual Positioning of the Underactuated Mobile Robot
**

**
Ruslan Sevostyanov
**

The paper is devoted to the problem of the positioning of the mobile robot in front of some external visual marker which is recognized by the video camera mounted on the robot. The task is complicated by the fact that the robot is underactuated. Algorithms which use the visual information directly in the feedback loop are well-known as visual servoing approach, but mostly such algorithms consider fully-actuated moving plants. Moreover, the considered algorithm uses the mathematical model of the robot's dynamics to enforce the control quality and also to use the special multipurpose structure of the feedback which allows meeting the set of requirements, particularly - the presence of the external disturbances. The results of the experiments with the computer model are given.

**
ID 044: Depth Control of an Unmanned Underwater Vehicle
**

**
Maria Smirnova, Mikhail Smirnov
**

The paper considers the problem of forming multi-purpose automatic control systems for a unmanned underwater vehicle. A system of ordinary nonlinear differential equations of the 12th order that describes the movement of an object as a controlled solid partially submerged in a liquid is formed. Controller for horizontal rudders in the mode of moving along a linear coordinate with the filter enabled, which provides a given value of trim during the transition to a given value of displacement in depth is formed.
To check the quality of the control law, a specialized software has been developed. Graphical results illustrating the effectiveness
of the developed method are performed.

**
ID 040: Marine Vehicles Automatic Control Based on Optimal Damping Concept
**

**
Evgeny Veremey, Margarita Sotnikova
**

This paper is devoted to the problems of feedback control laws design based on the optimization approach for marine vehicles. To provide desirable stability and performance features of nonlinear and nonautonomous closed-loop connections, it is proposed to construct design procedures using the optimal damping concept firstly developed by V.I. Zubov. Central attention is focused on the questions connected with practical implementation of the optimal damping methods for marine control systems. As an example, tracking problem is considered based on optimal damping control laws.

** ID 060: Multiplication Algorithm for Multivariate Trigonometric Series
**

**Levon Babadzanjanz, Irina Pototskaya, Yulia Pupysheva, Irina Alesova
**Multivariate trigonometric series are used for analytical and numerical solutions of a wide class of applied problems. This mathematical tool is in demand in celestial mechanics, quantum mechanics, electrical engineering, acoustics, optics, and the theory of signal and image processing. Multiplying such series when implementing numerical methods is a complex task that requires a large amount of machine time and memory. The formulas for the coefficients of the product of multivariate series derived in this article, can significantly reduce memory consumption and calculation time. Therefore, the using of these formulas in the software development to solve the mentioned tasks can improve its quality and competitiveness. All the results obtained are presented in the conclusion as final formulas for software implementation.

** ID 025: Application of Quasidifferential Calculus to Solving Optimal Control Problems with a Nonsmooth Functional
**

**Alexander Fominyh
**

The paper considers the problem of optimal control of an object described by a system with a continuously differentiable right-hand side and a nondifferentiable (but only quasidifferentiable) quality functional. We consider a problem in the form of Mayer with both a free and a fixed right end. Admissible controls are piecewise continuous and bounded vector-functions, which belong to a certain polyhedron at each moment of time. Standard discretization of the initial system and control parameterization are performed, and theorems on the convergence of the solution of the obtained discrete system to the desired solution of the continuous problem are presented. Further, for the obtained discrete system, the necessary and, in some cases, sufficient minimum conditions are written in terms of quasidifferential. The quasidifferential descent method is applied to this problem. The developed algorithm is demonstrated by examples.

#### Control and Optimization of Electro-Physical Processes, Part 2

##### Session FrA3. Chairs: Oleg Drivotin, Anna Golovkina

Location: Zoom ID: 922 5024 6030, https://youtu.be/7FxAmqeTntU

**ID 206: On the State Estimation of Non-linear Discrete Time Models
**

**
Mohamed Boutayeb, Abir Bouaouda
**

In this work we are interested in the state estimation of multi-variable non-linear discrete-time systems. The latter are obtained from the Leap-Frog discretization technique that may be applied to a large class of systems composed of nonlinear differential equations. This type of discretization induces a delay in the state space representation. Therefore a specific state space estimator without change of coordinates was established with convergence under weak conditions. In the second part of this work we are interested in the estimation of the position, orientation and speed of an Unmanned Aerial Vehicles (UAV) equipped with few sensors. From the observability condition, to assure convergence of the proposed state estimator, we show which physical variable should be measured.

**
ID 021: Field Emitters Periodic System on Substrate with Dielectric Layer Modeling
**

**
Ekaterina M. Vinogradova, Grigoriy G. Doronin
**

In this article a mathematical modeling of the 2D field emitters periodical system is presented. The uniform field emitters are located on a flat substrate. The substrate is covered with a dielectric layer. Anode is a plane parallel to the substrate. To calculate the electrostatic potential distribution in the entire region of the periodic system the unit cell with single field emitter is considered.
The effect of the field emitter on the electrostatic potential distribution is simulated as the effect of the charged line. Emitter surface coincides with zero equipotential.
To solve the boundary-value problem for the Poisson equation in the Cartesian coordinates the variable separation method is used.
The 2D analytical solution is obtained in the entire system area. The electrostatic potential distribution is presented in
the form of eigenfunction expansions.

**
ID 200: Genetic Stochastic Algorithm Application in Beam Dynamics Optimization Problem
**

**
Liudmila Vladimirova, Anastasiia Zhdanova, Irina Rubtsova, Nikolai Edamenko
**

The article discusses the application of the genetic global search algorithm to the problem of beam dynamics optimization. The algorithm uses normal distribution to form new generations and provides covariance matrix adaptation during random search. The method is easy to use because does not require calculation of the covariance matrix.
The algorithm is applied to global extremum search of the functional characterizing beam dynamics quality in linear accelerator. The extremal problem under study has a large number of variables; the objective function is multi-extreme. Therefore, the use of the stochastic method is preferred way to achieve the goal. The algorithm quickly converges and can be successfully used in solving multidimensional optimization problems, including its combination with directed methods. The optimization results are presented and discussed.

** ID 103: Factor Values Measurement and Heteroscedasticity by the Example of FEE Signal Identification
**

**Andrey Antonov, Nikolay Egorov, Marina Varayun'
**The problem of parametric identification of a field electron emission (FEE) signal is studied in the paper. The current response dependence on the voltage factor is investigated in terms of mathematical modeling by the least squares method. Attention is paid to the influence of the factor error on the parameters determination. It was found that after linearization of the response, the residuals of the regression model should show heteroscedasticity. At the same time, the autocorrelation effect was also checked. The Goldfeld-Quandt and Durbin-Watson tests, respectively, were performed. The significance of the regression model was monitored using Fisher's statistics. The normality of the residuals was investigated using the Shapiro-Wilk test.

#### Informatics and Control Processes, Part 2

##### Session FrB3. Chairs: Evgeny Veremey, Alina Boiko

Location: Zoom ID: 939 8906 7190, https://youtu.be/HD3xzv8WEGc

**ID 121: Spectral Design of H_2 Optimal Fault Detection Observer, Based on Modal Synthesis
**

**
Yaroslav Knyazkin
**

The main focus of this paper is design scheme of slowly varying additive fault detection observer-filters synthesis. It is necessary to suppress effect of the external disturbance, consisting of polyharmonic oscillation with given central frequency and a step function. A specialized spectral approach to the filter design, guaranteeing non-uniqueness of the optimal solution, is implemented to satisfy additional conditions, such as integral action. The improved modal synthesis technique, simplifying the design procedure, is proposed and a case study on marine ship longitude motion is given in the end to illustrate the proposed approaches with numerical simulation in MATLAB package.

**
ID 110: Adaptive Method for an Actuarial Optimal Control Problem with Dynamic Constraints
**

**
Alina Boiko
**

In this paper, we consider the application of a modern approach to solving nonlinear optimal control problems using as an example a relevant problem applied to the Russian insurance market. The actuarial problem is examined as an optimal control problem with dynamic constraints on the control. The approach for solving optimal control problems is based on R. Gabasov's adaptive method. The linear problem is reduced to an interval linear programming problem and the linear programming problem is solved by the adaptive method.

**
ID 069: Model of Stakeholders of the Socio-Cyber Physical System Life Cycle
**

**
Stanislav Mikoni
**

It was proposed to take the cyber-physical system as the core of the sociocyberphysical system, and the society for the external environment. The external environment is divided into representatives of society involved in the various stages of the life cycle of the cyber-physical system. The interests of the participants of the life cycle to the various properties of the cyber-physical system are defined. Taking into account these interests allows minimizing design errors at an early stage of shaping the appearance of the system. On the example of a truck, the heuristic structure of indicators and the structure representing the interests of the participants in its life cycle are compared.

**ID 195: Optimal Program Control in the Class of Quadratic Splines for Linear Systems
**

**
Alexander Popkov
**

This article describes an algorithm for solving the optimal control problem in the case when the considered process is described by a linear system of ordinary differential equations. The initial and final states of the system are fixed and straight two-sided constraints for the control functions are defined. The purpose of optimization is to minimize the quadratic functional of control variables. The control is selected in the class of quadratic splines. This is some evolution of the method when control is selected in the class of piecewise constant functions. Conveniently, due to the addition/removal of constraints in knots, the control function can be piecewise continuous, continuous, or continuously differentiable. The algorithm of solving consists in reducing the control problem to a convex mixed-integer quadratically-constrained programming problem, which could be solved using optimization methods by special software.

**ID 142: Kolmogorov Complexity-Based Similarity Measures to Website Classification Problems: Leveraging Normalized Compression Distance
**

**
Andrey Pechnikov, Anthony Nwohiri
**

World Wide Web has become the largest source for all kind of information thanks to its connectivity and scalability. With increasing number of web users and websites, the need for website classification becomes necessary. Due to its enormous size, fetching required information is a challenging task. Owing to the generality of topics, most links direct to websites or domains, instead of single webpages. Therefore, this paper proposes a new Kolmogorov complexity-based approach to website classification that leverages normalized compression distance to examine the similarity of websites. The approach is shown to have some prospects. To fully achieve the potentials of the approach, some questions need to be addressed before the approach could be automated for large-scale studies.

#### Closing Session & Open Microphone

##### Nikolay Smirnov, Anna Golovkina

Closing ceremony joint with an open microphone session where anyone can say some words about the experience during the conference, general impressions and give a feedback.

## Conference Proceedings

Papers for the conference proceedings will be selected by the program committee based on the results of the review and verification of the content originality.
The proceedings of SCP 2020 will be published by Springer in the series Lecture Notes in Control and Information Sciences - Proceedings.
**The papers of unmanned presentations will be excluded from the proceedings.**

The guidance for paper preparation can be found in the author section: Paper preparation.

Some presentations can be recommended by the program committee for extended version publication in the journal Vestnik of St. Petersburg University. Applied mathematics. Computer science. Control Processes indexed in Scopus and WoS.

## Keynote and Invited Speakers

**Prof. Leon Petrosyan**

Dean of the Faculty of Applied Mathematics - Control Processes (PM-PU),
Saint Petersburg State University.

Head of the department of Mathematical Game Theory and Statistical Decisions
(PM-PU).

** Talk: "On the Strong Time-Consistency of Set-valued Optimality
Principles"**

Born December 18, 1940 in Leningrad. Graduated from the Faculty of
Mathematics and Mechanics (Leningrad State University) in 1962, Ph.D., in
1965, Dr.Sci., in 1972. Since 1974 head of the Department of Mathematical
Game Theory and Statistical Decisions, and since 1975, dean of the Faculty
of Applied Mathematics and Control Processes.

**awards:**
Order of Friendship (1999), Medal of the Order for Merit to the Fatherland,
2-nd Class (2010), Laureate of the R. Isaacs Prize (2014)
Petrosyan L. A. is editor of the journals "Applied Mathematics, Computer
Science, Control Processes", "Mathematical Game Theory and its Applications"
and "International Game Theory Review".

From 1968 to 1969 he lectured and supervised the work of graduate students in
Egypt at Cairo and Asyut Universities. In 1974, 1980 and 1983, he lectured on
game theory at the University of Havana and the University of Santiago de
Cuba (Cuba); in 1979, lectures at the Humboldt and Dresden Technical
Universities (Germany); in 1990, at the University of California and Purdue
University (USA); in 1991, 1995, 1998 at the University of Tokyo,
universities in Osaka, Kobe, Hirasaki and Hiroshima (Japan); in 1992 - at
Stockholm University and at Stockholm Technical University; in 1994, 1995,
1996, 1997 at the University of Hamburg, Heidelberg, Munich Technical
University and the University of Ulm; in 1994, 1997, at Seoul University and
the University of Daegu City (Korea); in 1994, 1995, 1996, 1997, 2012, 2015
at the University of Montreal (Canada); in 1998 at the Hebrew University of
Jerusalem (Israel); in 1998 at Cambridge and London universities (Great
Britain); in 2004, 2010, 2012, 2015 at the University of Hong Kong, as well
as in Xi'an, Harbin, Beijing and Qingdao University (China).
Personal page

**Prof. dr. ing. Vladimir Rasvan**

Director of the doctoral school, Faculty of Automation, Computers and Electronics, Craiova University, Romania

**Talk: Systems with Propagation: a Bunch of Models and a Research Programme**

There are discussed here several applications of Physics and Engineering which are described by 1D propagation - hyperbolic partial
differential equations in two dimensions (time and one space dimension for distributed parameters) having nonlinear and nonstandard boundary conditions. Nonstandard boundary conditions means they
contain ordinary differential equations. It is presented the association of a system of functional differential equations and the one to one correspondence between the
solutions of the two mathematical objects. In most cases the functional differential equations thus associated are of neutral type having (sometimes) a marginally stable
difference operator. A set of open problems for these equations is listed.

**Prof. Sorin Olaru**

Professor, Laboratory of Signals and Systems, CentraleSupelec - University Paris Saclay, France

**Talk: From Control Invariant sets to an Inverse Optimality Perspective on the Constrained Control Design**

**Abstract:**
This talk will review some of the early works on constrained control underlining their influence on the latest optimization-based control
design methodologies. We will trace the path from vertex controllers, to predictive control and ultimately to interpolation-based control.
Interestingly, we will point to the relationship between these techniques and the optimality of a certain performance index that can be interpreted
as a Lyapunov function but also geometrically as a convex lifting over the system's state space. This last perspective makes a link to the inverse
optimality argument for any stabilizing control law. Finally, we will point to the parameter uncertainty in dynamical models as part of such an
inverse-optimal control policy and discuss some open problems.

**Bio:** Sorin Olaru is a Professor and head of the RTE Chair at CentraleSupelec,
and member of the CNRS Laboratory of Signals and Systems, all these organizations being part of the Paris-Saclay University in France.
He held research positions or has been invited scientist at INRIA in France, NTNU in Norway, Univ. of Newcastle in Australia,
Kyushu Institute of Technology in Japan, FIAS in Germany. His research interests are encompassing the optimization-based control design,
set-theoretic characterization of constrained dynamical systems as well as the numerical methods in optimization and control.
He is currently involved in research projects related to embedded predictive control, fault tolerant control and networked (time-delay) control systems.

**Prof. Noboru Sakamoto**

Professor, Science and Engineering Department, Nanzan University, Nagoya, Japan

**Talk: "A dynamical system view on nonlinear optimal control analysis and design"**

Received the B.S. degree in Mathematics from Hokkaido University (1991)
and M.S. and PhD degrees in Aerospace Engineering from Nagoya University (1993 and 1996, respectively).
From 1996 until 2015, he held positions in the Graduate School of Engineering in Nagoya University.
Currently, he is a Professor with the Science and Engineering of Nanzan University in Nagoya, Japan.
He has held a visiting research position at University of Groningen, The Netherlands, in 2005 and 2006.
He received the SICE Best Paper Prizes in 1997, 2006, 2008 and 2011 and SICE Kimura Prize in 2016.

**Prof. Alexander Fradkov**

Professor, Department of Theoretical Cybernetics, Saint Petersburg State University,

Head of the Laboratory of Complex Systems Control, Institute for Problems of Mechanical Engineering of the Russian Academy of Sciences,

Professor, Saint Petersburg National Research University of Information Technologies, Mechanics and Optics,
Saint Petersburg, Russia

**Talk: "Adaptation and Learning: a Brief History"**

Machine learning and artificial intelligence have attracted a lot of attention during recent
years. They are applied to various new problems and it looks like they are based upon
completely new ideas in the applied science. However there exist strong links
between machine learning and classical adaptation methods which are much lesser known
and almost not exploited nowadays. In this talk a brief overview of the historical evolution of the machine learning field
and its relations to adaptation, optimization and adaptive control are discussed.
A number of little-known facts published in hard-to-reach sources are presented.