Solution and Optimal Strategies for a Differential Game of Pursuit-Evasion with Point-Wise Constraints

Abstract

This work study a differential game of pursuit-evasion involving countably many pursuers $p_{1},p_{2},\cdots,p_{m}$ and a single evader $e$ under point-wise (geometric) constraints in the sequence space $l_{2}.$ The pursuers evolve according to specified differential equations of $1^{st}$ order while the evader follows a $2^{nd}$ order differential equation. The game period is a fixed time interval of length $θ$ unit of time. The minimum distance between evader and the pursuer at the terminal time denotes the game payoff. The pursuers aim is to minimize the payoff, whereas the evader seeks to maximize it. We obtain the solution of the game, including optimal strategies of the players construction, as well as game value estimation.