Fuzzy Fault-tolerant Controller With Guaranteed Performance for MIMO Systems Under Uncertain Initial State

Abstract

It is always problematic that the initial value of the trajectory tracking error must be inside the area included in the prescribed performance constraint function. To overcome this problem, a novel fault-tolerant control strategy is designed for a second-order multi-input and multi-output nonlinear system (MIMO-NLS) with unknown initial states, actuator faults, and control saturation. Firstly, a predefined time convergence (PTC) stability criterion is theoretically proven. Then, an error conversion function is introduced to convert the trajectory tracking error to a new error variable with an initial value of zero, and an adaptive fuzzy system is designed to approximate the compound interference composed of actuator fault, parameter perturbation, control saturated overamplitude, and external disturbance. Based on the backstepping control method, prescribed performance control method, and predefined time convergence stability theory, an adaptive fuzzy fault-tolerant controller for the new error variable is designed and theoretically proven for the predefined time convergence of the closed-loop system. The numerical simulation results of the guaranteed performance trajectory tracking control for industrial robots with actuator faults demonstrate that the adaptive fuzzy fault-tolerant control algorithm has strong fault tolerance to actuator faults and anti-interference capabilities. The convergence time and performance of trajectory tracking errors can be preset in advance, and the parameter settings of the prescribed performance constraint function are not affected by the initial state values.