Group Pursuit Problem in a Differential Game with Fractional Derivatives, State Constraints, and Simple Matrix

Abstract

In a finite-dimensional Euclidean space, we consider the pursuit problem with one evader and a group of pursuers described by a system of the form D^(α)z_i = az_i + u_i - v, where D^(α)f is the Caputo derivative of order α ∈ (1, 2) of a function f. The set of admissible solutions u_i and v is a convex compact set, the objective set is the origin, and a is a real number. In addition, it is assumed that the evader does not leave a convex polyhedral cone with nonempty interior. We obtain sufficient conditions for the solvability of the pursuit problem in terms of the initial positions and the game parameters.