Control Strategies in the Problem of Approach of Conflict-Controlled Objects

The authors propose a new approach to generating control strategies in the problem of approach of conflict-controlled objects. Modifications of the first direct method are 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 formulating the results and can be determined in the general case 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 when the classical Pontryagin’s condition is not satisfied. The guaranteed times are compared for different schemes of the considered methods. The theoretical results are illustrated on a second-order model example with a special non-convex control domain of the pursuer.