Target–Attackers–Defenders Linear–Quadratic Exponential Stochastic Differential Games With Distributed Control

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.