Approximate construction of solutions in game-theoretic control problems

The problem of control using the feedback principle is considered, in which the aim is to ensure that a phase point falls within a terminal set no later than a specified time for any noises acting on the system, which are unknown in advance [1]. A method for the approximate construction of the set of positional absorption, that is, the set of all initial points for which the problem is solvable, is proposed. The relations defining the approximate set of positional absorption are stated. These relations differ from those proposed in [2] for the problem of approaching the terminal set at a given time. The results of an approximate computation of the set of positional absorption in the problem of controlling a pendulum in a viscous medium are presented. The paper touches on the topics considered in [1-16]. (C) 1997 Elsevier Science Ltd. All rights reserved.