Partially observed multi-player stochastic differential games under directed graphs

This paper is concerned with the multi-player stochastic differential pursuit-evasion game problem based on directed graphs. To solve the challenges posed by limited communication and ubiquitous noise, a novel Riccati equation is proposed based on the linear–quadratic exponential cost function under both complete and partial observations. The optimal strategies for pursuers and evaders are obtained based on the direct method of completing the square and Radon–Nikodym derivative, without the need to solve the complex Hamilton–Jacobi–Isaacs equation. The strategy presented in this paper is distributed and can be implemented without requiring any global information, under the constraints of a directed topology. Additionally, the proposed partial algorithm introduces an information filter to estimate partial observations. We also demonstrate that the proposed strategy constitutes a Nash equilibrium. Numerical simulations confirm the effectiveness of our strategy in both complete and partial observation scenarios.