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.