Target–Attackers–Defenders Linear–Quadratic Exponential Stochastic Differential Games With Distributed Control
研究了多个攻击者、防御者与单个目标之间的随机微分博弈，利用拓扑图论设计无需全局信息的分布式控制策略，通过直接平方完成法和Radon-Nikodym导数推导出两种场景下的最优控制，并验证了其能驱动系统达到纳什均衡。
This article investigates stochastic differential games involving multiple attackers, defenders, and a single target, with their interactions defined by a distributed topology. By leveraging principles of topological graph theory, a distributed design strategy is developed that operates without requiring global information, thereby minimizing system coupling. Additionally, this study extends the analysis to incorporate stochastic elements into the target-attackers-defenders games, moving beyond the scope of deterministic differential games. Using the direct method of completing the square and the Radon-Nikodym derivative, we derive optimal distributed control strategies for two scenarios: one where the target follows a predefined trajectory and another where it has free maneuverability. In both scenarios, our research demonstrates the effectiveness of the designed control strategies in driving the system toward a Nash equilibrium. Notably, our algorithm eliminates the need to solve the coupled Hamilton-Jacobi equation, significantly reducing computational complexity. To validate the effectiveness of the proposed control strategies, numerical simulations are presented in this article.