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 const ruction of the set of positional absorption, that is, the set of all i nitial points for which the problem is solvable, is proposed. The rela tions 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 appro ximate 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.