CONTROL STRATEGIES IN THE PROBLEM OF APPROACH OF CONFLICT-CONTROLLED OBJECTS

Abstract

The authors propose a new approach to forming control strategies in the problem of approach of conflict-controlled objects. Modifications of the first direct method is developed for the stroboscopic strategy in the class of counter-controls where the classical Pontryagin’s condition is not satisfied. The lower resolving function is considered, which plays a key role in the formulation of the results and in the general case can be determined using the Minkowski functional of a multivalued mapping. An upper resolving function is introduced and a modified scheme of the method of resolving functions is proposed, which guarantees the termination of the conflict-controlled process in the class of quasi-strategies and counter-controls where the classical Pontryagin’s condition is not satisfied. The guaranteed times for different schemes of the considered methods are compared. The theoretical results are illustrated on a second-order model example with a special non-convex control region of the pursuer. Keywords: control strategy, resolving function, dynamic game problem, problem of approach of controlled objects.