Integrated Robust Control and Approximate Dynamic Programming for Spacecraft Pursuit-Evasion Games under Uncertain Dynamics

To address spacecraft pursuit games in uncertain dynamic space, this paper presents an integrated solution combining robustness analysis and Adaptive Dynamic Programming (ADP). Firstly, a nonlinear relative motion model considering environmental disturbances and target uncertainties is built. Its robustness is enhanced via dimensionless treatment and stochastic disturbance design. Based on lyapunov and Hamilton-Jacobi-Isaacs (HJI) equations, robust optimal control laws for single spacecraft and Nash equilibrium strategies for multi-spacecraft cooperation are devised to ensure asymptotic stability under disturbances. To overcome computational challenges in large state spaces, an ADP framework with Support Vector Regression (SVR) is used. By multi-moment approximation with linear basis functions, efficient policy iteration in a finite time domain is achieved. Numerical simulations show the proposed method performs excellently in spacecraft pursuits, adjusting control commands in real-time against external disturbances and ensuring mission success rates.