Fixed-Time Fuzzy Sliding Mode Control of Nonlinear Systems with Stochastic Processes

This paper stresses the fixed-time sliding mode control (SMC) problem of a class of nonlinear systems with Markov stochastic process. The fuzzy model is used to approximate the nonlinear systems. A fuzzy integral-type sliding variable is utilized and then the fixed-time reachability of the ideal sliding mode is analyzed. In the sliding mode, that the system states converge into a steady state set in a fixed time can be ensured by some designed solvable conditions of the controller parameters. Compared with traditional SMC, the upper bound of the entire settling time is fixed, including the reaching time and the sliding time during the control process. Finally, the effectiveness of the presented control strategy is verified through a set of numerical simulation experiments.