On linear differential games of pursuit in the class of positional countercontrols

N. L. Grigorenko

Lomonosov Moscow State University

Abstract: A linear conflict-controlled process of two players with a terminal set in the form of the sum of a linear subspace and a convex compact in its orthogonal complement is considered. The process is considered from the point of view of the first player. Its goal is to bring the controlled object to the terminal set. It is assumed that the first player knows the dynamic characteristics of the controlled object, the phase variables and the control of the second player. Sufficient conditions are presented under which the first player can guarantee the bringing of the phase vector of the game to the terminal set. A form of positional counter-control of the first player guaranteeing the completion of the process is given. Such positional counter-control is intended for operation in the logic of step-by-step positional control of a combined system including a real controlled object and a model (guide) and implementing tracking of the guide's movement in the form of an extreme aiming procedure implemented step-by-step in a discrete system and having resistance to information interference, achieved in a scheme with a guide. Examples are considered.

Keywords: differential games, positional control, counter-control, positional counter-control, object bringing problem, structural synthesis, guide control, analytical design of aggregated controllers.

UDC: 517.977

MSC: 91A23, 91A24, 91A80

Received: 17.01.2025
Revised: 14.04.2025
Accepted: 21.04.2025

DOI: 10.21538/0134-4889-2025-31-2-69-80

Bibliographic databases:

•