Neural-network sliding mode control of nonlinear systems via a fuzzy integral switching function

In this paper, a fuzzy neural-network sliding mode control (FNNSMC) problem for nonlinear systems is investigated utilizing a fuzzy integral switching function (FISF). Different from the previous work on integral sliding mode control (ISMC), four terms are included in the designed FISF, which deeply merges the characteristics of the fuzzy membership functions (FMFs). The FMFs and state variables are used to design the first two terms of a FISF. An integral term on a derivative of the FMFs is considered to design the last term, which can reflect more features of fuzzy systems compared with the existing methods. Subsequently, combining with the designed FISF, a Gaussian radial basic neural network is used to devise a FNNSMC law, which can effectively mitigate the amplitude of the high-frequency chattering. Additionally, a fuzzy Lyapunov method and a switching idea are employed to analyze the asymptotical stability of the sliding motion, which can reduce the conservatism of the stability criteria. In the end, the availability and advantages of the proposed theoretical results can be verified via some simulations.