Fuzzy Fault-Tolerant Predefined-Time Control for Switched Systems: A Singularity-Free Method

The subject of this study is fuzzy predefined-time control for a class of switched nonlinear systems with multiple faults. In comparison to existing research on predefined-time control, this study delves into the realm of switched nonlinear systems, encompassing switched linear sensor faults and switched nonaffine faults. The difficulty in the controller design lies in following the backstepping technique, as taking the derivative of fractional power virtual control laws would trigger singularity issues at equilibrium states or coordinate transformation origins. The study utilizes the unique characteristics of switching and fuzzy logic systems to introduce a continuous piecewise predefined-time controller with a fault-tolerant compensation mechanism to avoid singularity problems. By adjusting a predefined parameter in the developed controller, the system could achieve the objectives of adaptive stability and adaptive tracking within a predefined time, as desired by the user. Moreover, the application of the proposed algorithm to practical systems is presented.