A SOSM control algorithm by using fixed-time adaptive fuzzy technique

In this paper, a fixed-time adaptive fuzzy second-order sliding mode (SOSM) controller is designed for the nonlinear systems with output constraints. The fuzzy logic system is used to approach the unknown bound of uncertainties dynamically. First of all, a control method which can be used to solve the problems of the output constraints has been proposed through constructing a barrier Lyapunov function and applying the technique of adding a power integrator. Next, by using the adaptive fuzzy method, the problem of chattering can be handled. Then, with the help of the fixed-time control theory, a fixed-time adaptive fuzzy SOSM controller is presented. The proposed method can expedite the sliding variables to be stabilized to zero in fixed time no matter how the initial values change. Meanwhile, it can also constrain the output variables in the specified region without crossing the boundary at the beginning. Moreover, by using a strict Lyapunov stability analysis, the sliding variables can converge to zero in fixed time.