Optimal Control Strategies in Multi-Pursuit-Multi-Evasion Differential Games with Communication Graphs

Traditional pursuit-evasion (PE) games predominantly rely on infinite-time formulations, which ignore real-world demands and practical communication constraints. In this paper, a finite-time pursuit-evasion conflict in multi-pursuer-multievader (MPME) nonzero-sum game framework with a communication-weighted matrix Q is proposed, reflecting the practical communication topology. In such circumstances, a novel sufficient condition for uniform exponential stability is proved for all-against-all games and the optimal control strategies for all players are derived by solving the coupled Hamilton-Jacobi-Isaacs (HJI) equations associated with the MPME game, thereby enabling the attainment of Nash equilibrium under finite-time state regulation. Finally, numerical experiments involving three pursuers and two evaders are carried out, which validates the effectiveness of the proposed method.