A Differential Game Problem of Many Pursuers and One Evader in the Hilbert Space $$\ell_2$$

Abstract

In this paper, we investigate a differential game problem of multiple number of pursuers and a single evader with motions governed by a certain system of first-order differential equations. The problem is formulated in the Hilbert space $$\ell_2,$$ with control functions of players subject to integral constraints. Avoidance of contact is guaranteed if the geometric position of the evader and that of any of the pursuers fails to coincide for all time t. On the other hand, pursuit is said to be completed if the geometric position of at least one of the pursuers coincides with that of the evader. We obtain sufficient conditions that guarantees avoidance of contact and construct evader’s strategy. Moreover, we prove completion of pursuit subject to some sufficient conditions. Finally, we demonstrate our results with some illustrative examples.