Fault-tolerant tracking control for nonlinear systems with multiplicative actuator faults in view of zero-sum differential games

Abstract

In view of zero-sum differential games, this paper addresses the fault-tolerant tracking control (FTTC) problem for nonlinear systems with multiplicative actuator faults. By augmenting the nominal system, the trajectory tracking problem is transformed into an optimal regulation problem. A fault observer is designed to estimate the multiplicative actuator fault factor. In order to better reflect system performance, a comprehensive performance index function including the trajectory tracking error, the control input, and the multiplicative actuator fault is constructed. By considering the control input and the multiplicative actuator fault as two players in the zero-sum differential game (ZSDG), the FTTC problem is thus transformed into a ZSDG problem. Then, a fault-tolerant control based on ZSDG is designed by solving the Hamilton–Jacobi-Isaacs (HJI) equation. Since the HJI equation is difficult to solve, a critic neural network is constructed to obtain its approximation, which constitutes the Nash equilibrium of the ZSDG. The closed-loop faulty system is guaranteed to be uniformly ultimately bounded via the Lyapunov’s direct method. The effectiveness of the developed FTTC method is demonstrated by two simulation examples.