Pursuit Problem of a Linear Differential Game for Many Numbers of Players with Geometric and Gronwall Type Constraints on Players Controls

In this paper, we study a Pursuit differential game with many number of pursuers and evaders in \(\mathbb{R}^n\) The player’s motion obey linear differential equations and the control functions of pursuers and evaders are subject to Geometric and Gronwall constraints respectively. If the pursuer’s state and the evader’s state coincide, the game is deemed completed. We construct a strategy that is distinct from a parallel approach strategy that guaranteed pursuit completion and demonstrated sufficient conditions for which pursuit is completed for many number of pursuers and evaders.