Fixed Time Adaptive Fuzzy Control of Nonlinear Systems with Time-Varying State Constraints

In this paper, a fixed-time adaptive fuzzy control scheme is investigated to stabilize a class of uncertain nonlinear systems with full-state constraints. A novel secant barrier Lyapunov function (SBLF) is first constructed to design the controller and obtain the fixed-time stability properties by using the (SBLF) in the design process of back-stepping. The adaptive controller is presented to guarantee that the tracking errors of the system can converge into the neighborhood around the equilibrium point in a fixed time and all the system states can be restricted within the predefined time-varying boundaries. By making use of Lyapunov analysis, we can prove that all the signals in the closed loop system are uniformly ultimately bounded and the output is well driven to follow the desired trajectory. Finally, simulations are given to verify the effectiveness of the method.