Nonlinear Control for Spacecraft Pursuit-Evasion Game Using the State-Dependent Riccati Equation Method

Spacecraft pursuit-evasion game is formulated as a two-player zero-sum differential game. The Hill reference frame is used to describe the dynamics of the game. The goal is to derive feedback control law which forms a saddle point solution to the game. Both spacecraft use continuous-thrust engines. The linear quadratic differential game theory is applied to derive a linear control law. This theory is extended to derive a nonlinear control law using the state-dependent Riccati equation method. A state-dependent coefficient matrix is developed for this purpose. Various scenarios are considered for comparing the performance of the linear and nonlinear laws. In all the scenarios, the efficacy of the nonlinear control law is found to be superior to that of the linear control law with computation cost similar to the linear law.