V.N. Ushakov

On a computational algorithm for solving game control problems

Abstract A positional differential game of approach to a target is considered. The construction of the set of positional absorption (SPA) is studied. Relations are given, on the basis of which an algorithm of approximate computation of the SPA for controlled systems in the plane is developed.

On solving approach problems for control systems

We study the problem of making a control system in a finite-dimensional Euclidean space approach a compact set at a fixed instant of time. The technique presented in the paper for solving the approach problem is based on constructions involving solvability sets. To construct approximately the solvability set, we apply a backward (in time) procedure that involves storing controls selected during the construction of this set. We also give examples of simulation of approach problems for mechanical systems.

Differential games with fixed terminal time and estimation of the instability degree of sets in these games

This paper contributes to the theory of differential games. A game problem of bringing a conflict-controlled system to a compact target set is analyzed. Sets in the position space that terminate on the target set and are not stable bridges are considered. The notion of stability defect of these sets is examined. It is demonstrated how the notion of stability defect can be used to construct sets with relatively good geometry that are at the same time convenient for the first player to play the game successfully.

On the notion of stability defect in game control problems

The stability property in a game problem of the approach of a conflict-controlled system to a target set at a fixed terminal moment is investigated. The notion of a stability defect is introduced for sets in the space of game positions.

Positional procedures for solving dynamical optimization problems of prescribed duration

Abstract Optimal control problems under conflict or uncertainties are considered on a finite time interval. Resolving dynamical procedures are suggested. They are based either on constructions of stable bridges produced with the help of step-by-step programmed absorptions or on applications of the backward dynamic programming method. Results of simulations illustrating the suggested methods are exposed.

On the Problem of an Approach to a Non-Cylyndrical Target1

Abstract The differential game of an approach to a compact set on fixed time interval with players’ controls constrained to geometric restrictions is considered. The target set is supposed to be non-cylindrical, i.e. dependent on time. Constructing an approximating system of sets, which approximates the maximal minimaxly u-stable bridge, is realized on the base of backward procedures. This results can be used in the development of methods for numerical constructing stable bridges.