Terminal Orbital Adaptive Dynamic Programming-based Control for Satellite Pursuit Evasion Game with Input Saturation

TL;DR: A novel single-network adaptive dynamic programming method is proposed to solve the terminal pursuit-evasion control problem with input saturation. The method utilizes a non-quadratic cost function and a single-network structure to obtain the optimal controller. Lyapunov theory guarantees the convergence of weights and stability of the closed-loop system.

Abstract: A continuous space pursuit-evasion game algorithm based on zero-sum game is proposed to solve the problem of the terminal pursuit-evasion control of spacecraft with input saturation. A novel single-network adaptive dynamic programming method is proposed to obtain the solution of zero-sum game. Firstly, it is assumed that the two satellites are close such that the nonlinear dynamics could be reduced to the CW equations. Considering the input saturation, a non-quadratic cost function is proposed to formulate a Hamilton-Jacobi-Isaacs equation. Then, only a critic neural network is employed to learn the optimal value function and further obtain the optimal controller, which enables the architecture of adaptive dynamic programming implementation to be simpler. An NN weight updating law is constructed, by which the restriction of initial admissible control is removed. Based on the Lyapunov theory, the convergence of critic NN weights and the stability of closed-loop system are guaranteed. Finally, numerical results verify the efficiency of the proposed method.