Conditional Sliding Mode Control-Based Fixed-Time Stabilization of Fuzzy Uncertain Complex System

This work explores the fixed-time stabilization of fuzzy uncertain systems based on conditional integral sliding mode control. The difficulties in solving such problems include the integral windup problem and the severe chattering problem when the system converges. Moreover, the design of the traditional fixed-time controller algorithm in the integral sliding mode control becomes complicated. In order to overcome these difficulties: 1) a piecewise function which can bring distant states closer to the sliding surface is considered in the integral function to prevent the integral windup problem, 2) a class of state variable controllers with odd power is designed to solve the chattering problem due to there is no sign function, 3) a fixed-time control algorithm is introduced into the integral function and the controller to guarantee that both the reachability and sliding motion phases are fixed-time stable. Furthermore, based on 1) and 3), an appropriate fixed-time conditional integral sliding mode controller is constructed to ensure the fixed-time reachability of the designed sliding mode surface. Besides, combining 1), 2) and 3), a class of chattering-free fixed-time integral sliding-mode controllers is established to obtain the fixed-time reachability of the sliding mode surface and the fixed-time stability of sliding mode dynamics. This method dramatically reduces the chattering problem and can adjust integral windup. Finally, two numerical simulations are presented to verify the theoretical results, showing the robustness of the designed overshoot factor and the chattering-free scheme for sliding mode control.