A Discrete Game Problem with a Non-convex Terminal Set and a Possible Breakdown in Dynamics

Abstract

A one-dimensional discrete game problem with a given endpoint is considered. A terminal set is a union of an infinite number of disjoint segments of equal length. This terminal set has the meaning of the neighborhood of the desired state of the system, taking into account the periodicity. It is believed that one breakdown is possible, which leads to a change in the dynamics of the controlled process. The breakdown time is not known in advance. The first player’s control is based on the principle of minimizing the guaranteed result. The opposite side is the second player and the moment of the breakdown. In this paper, we have found necessary and sufficient termination conditions and constructed the corresponding controls of the players. As an example, we consider the problem of controlling a rotational mechanical system with disturbance and possible breakdown. KeywordsGameControlBreakdown