Predefined-Time Fault-Tolerant Control for a Class of Nonlinear Systems With Actuator Faults and Unknown Mismatched Disturbances

Predefined-time control has made great progress in recent years, but its current techniques have limitations in their applicability to systems experiencing mismatched disturbances, and has yet to resolve some issues regarding fault-tolerant control (FTC). This paper is concerned with a practical predefined-time fault-tolerant tracking control problem for high-order strict-feedback nonlinear systems subject to actuator faults and unknown mismatched disturbances. In this study, the exact information of actuator faults and the bound of the disturbances are unknown. By applying a predefined-time stability theory, a novel backstepping-based predefined-time fault-tolerant tracking control approach is developed. Incremental vectors about disturbances are constructed, and adaptive laws are designed to compensate for the effects of the disturbances and faults. To further handle the problem of the computational explosion, a novel command-filtered FTC scheme of predefined-time tracking is employed to decrease the calculation burden. With the proposed fault-tolerant controllers, all signals in the closed-loop system are bounded, and the output tracking error is guaranteed to converge into a user-defined set within a predefined interval. Simulation studies are carried out to demonstrate the performance of the designed controllers. Note to Practitioners-Numerous practical systems, such as manipulator arms, circuit systems, and electromechanical systems, among others, can be modeled as strict-feedback nonlinear systems. These systems are vulnerable to external disturbances and actuator faults during operation. To maintain system efficiency after a fault occurrence or to fulfill specific task requirements, tracking control must satisfy specific constraints on time response. In this paper, a practical predefined-time FTC method is proposed for strict-feedback nonlinear systems with actuator faults and mismatched disturbances. Furthermore, a predefined-time FTC scheme with a low computational effort is developed, specifically tailored for high-order systems. The designed controllers are suitable for practical systems that can be modeled in strict-feedback form with known dynamics. For more complex nonlinear systems with unknown dynamics and strong nonlinearity, the approaches proposed in this paper may no longer be suitable. Future research will focus on designing and applying predefined-time fault-tolerant controllers for specific complex practical systems, taking into account their characteristics and uncertainties.