Valery Afanasiev

Automation. Modern Technologies

The optimal control problem formulated for a class of nonlinear objects that can represented as objects with a linear structure and state-dependent parameters. The linear structure of the transformed nonlinear system and the quadratic quality functional allow us to switch from the need to search for solutions of the Hamilton-Jacobi equation to a Riccati-type equation with state-dependent parameters in the synthesis of optimal control. The main problem of implementing optimal control is associated with the problem of finding a solution to such an equation. The article proposes an algorithmic method of parametric optimization of the controller, based on the use of the necessary optimality conditions for the considered control system. The constructed algorithms can be used both for optimization of non-stationary objects themselves, if the corresponding parameters are selected for this purpose, and for optimization of the entire controlled system with the help of the corresponding parametric tuning of the controllers. The effectiveness of the developed algorithms demonstrated by the example of drug treatment of patients with HIV.

Automation and Remote Control, 2021, 82(2), 245-263 рр.

DOI
10.1134/S0005117921020053

A differential game of several players is considered as follows. One player (attacker) penetrates some space, and several other players (pursuers) appear simultaneously to intercept the attacker. Upon detecting the pursuers, the attacker tries to evade them. The dynamics of each player are described by a time-invariant linear system of a general type with scalar control. A quadratic functional is introduced, and the differential game is treated as an optimal control problem. Two subproblems are solved as follows. The first subproblem is to construct a strategy for pursuing the attacker by several players having complete equal information about the game. The second subproblem is to construct such a strategy under incomplete information about the attacker actively opposing the pursuers. The simulation results are presented. The zero-sum differential game solution can be used for studying the final stage of pursuit, in which several pursuers and one evader participate.

Control Sciences. 2021. №1.21-30 рр DOI: http://doi.org/10.25728/cs.2021.1.3

We consider the problem of a zero-sum differential tracking game with a quadratic
performance functional in which the plant subjected to uncontrolled disturbances is described by a nonlinear ordinary differential equation. The synthesis of optimal controls is known to necessitate online solving a scalar Bellman–Isaacs partial differential equation that contains information about the trajectory of the process to be monitored. The lack of information about this process over the entire control interval makes the synthesized controls unimplementable. An algebraic method is proposed for solving the Bellman-Isaacs equation, which contains the current value of the monitored process. As an illustration of the results obtained, we give the simulation of the behavior of a nonlinear system with two players with an open control horizon.

From 1972 to present - assistant, senior lecturer, associate professor, professor.
Time work: departamena professor of applied mathematics at the Moscow Institute of Electronics and Mathematics.

Visiting Professor (2002-2010): The Bauman Moscow Technical University. Russian University of Peoples' Friendship.

Since 2011, Professor (on conditions of part-time) at Moscow State University (Department of Physics)

Mathematical Theory of Control Systems Design. V.N. Afanas’ev, V.B. Kolmanovskii, V.R. Nosov. Kluwer Academic Publisher. Dordrecht/Boston/London. 670 p.

The book is based on several courses of lectures on control theory and applications which were delivered by the authors for a number of years at Moscow Electronics and Mathematics University.

V.N. Afanasiev Control of uncertain dynamic objects. Moscow. Fimatlit. 2008. 208 p.

The book examines the controlled systems, which describe the behavior of linear and nonlinear differential inclusions with fuzzy given initial conditions.

V. N. Afanasiev. Control uncertain nonlinear dynamic objects

The book is devoted to a systematic exposition of the methods of mathematical design of nonlinear uncertain dynamical systems, systems can be represented with parameters depending on the state. Material book may be of interest for professionals working in the management of a variety of objects, as well as for students and postgraduates of relevant specialties.