Sufficient Convergence Conditions for Conflict Controlled Objects with Different Inertia

The problem of approach of controlled objects with different inertia in dynamic game problems is considered. For such controlled objects, it is characteristic that the Pontryagin condition is not satisfied on a time interval. To solve the problem, a special multivalued mapping and a matrix function are introduced to equalize the players’ control resources, and then the additional resource is compensated by the body component of the cylindrical terminal set. With the use of the lower resolving function for objects with different inertia, two modified schemes of the first direct Pontryagin method are proposed, which guarantee the successful completion of the conflict-controlled process in the class of countercontrols. The upper resolving function is introduced, and the corresponding modified schemes of the method of resolving functions are presented for controlled objects with different inertia in the class of quasi-strategies and counter-controls. New theoretical results are illustrated by a model example.