Multi-Player Linear-Quadratic Exponential Stochastic Differential Games on Directed Graphs

To solve the problem caused by limited communication and ubiquitous noise, we formulate the multi-player stochastic differential pursuit-evasion games based on directed graphs. This paper proposes a novel Riccati equation concerning multi-player stochastic differential games based on the linear-quadratic exponential cost function. We define capture and escape conditions for pursuers and evaders, respectively. Subsequently, the optimal strategies for pursuers and evaders are obtained based on the communication topologies and a direct method using completion square and Radon-Nikodym derivative. Under the constraints of directed topology, the strategy presented in this article is distributed, and players do not require any global information. Besides, we provide sufficient theoretical evidence that the proposed strategy is a Nash equilibrium. Numerical simulations verify the effectiveness of the strategy in capture scenarios and escape scenarios.