Fixed-time adaptive fuzzy SOSM controller design with output constraint

A fixed-time adaptive fuzzy second-order sliding mode (SOSM) approach has been designed to handle the problem of nonlinear systems with output constraints. According to the advantages of using fuzzy logic systems, the unknown bounds of uncertainties can be approached dynamically. The problem of output constraints has been well handled by constructing a barrier Lyapunov function. Next, with the help of adding a power integrator technique and adaptive fuzzy control, a fixed-time adaptive fuzzy SOSM controller is designed for the considered systems. In addition to the above, the controller can not only promote the sliding variables to converge to the origin in fixed time, but also stabilize the variables in the constrained range. In other words, under the proposed method, the systems can be stable in a specified time no matter how the initial value changes. Lastly, a numerical example is used to verify the performance of the proposed SOSM control tactic.