Zero-Sum Differential Game-Based Fault-Tolerant Control for a Class of Affine Nonlinear Systems

This article proposes a zero-sum differential game-based control scheme for a class of affine nonlinear control systems with actuator faults, including loss of control, loss of effectiveness, and bias faults. In the control design, the bias faults and the control signal are chosen as the two opposite sides. The Nash equilibrium is achieved while the optimal control signal and the upper bound of bias faults can be derived from the Hamilton-Jacobi-Isaacs (HJI) equation. An adaptive dynamic programming (ADP) method is employed to estimate the weight of the critic network. The developed zero-sum differential game-based control scheme can ensure the system stability and optimal performance. Two simulation results on a numerical system and a rigid spacecraft model illustrate the effectiveness of the proposed control scheme.