Construction of a maximal stable bridge in games with simple motions on the plane

Abstract

It is known that the solvability set (the maximal stable bridge) in a zero-sum differential game with simple motions, fixed terminal time, geometric constraints on the controls of the first and second players, and convex terminal set can be constructed by means of a program absorption operator. In this case, a backward procedure for the construction of t-sections of the solvability set does not need any additional partition times. We establish the same property for a game with simple motions, polygonal terminal set (which is generally nonconvex), and polygonal constraints on the players’ controls on the plane. In the particular case of a convex terminal set, the operator used in the paper coincides with the program absorption operator.