Hierarchical fuzzy sliding-mode control for uncertain nonlinear under-actuated systems

This paper presents a hierarchical fuzzy sliding mode control scheme for a class of uncertain nonlinear under-actuated systems. First, the sliding surface of one subsystem is selected as the first layer sliding surface. Hence, we further construct a second layer sliding surface from the first layer sliding surface and the sliding surface of another subsystem till all the subsystem sliding surfaces are included. The fuzzy system and some adaptive laws are applied to approximate the unknown nonlinear functions and estimate the upper bounds of the unknown uncertainties, respectively. By means of Lyapunov stability theorem and the theory of sliding mode control, the proposed control scheme ensures the robust stability of the uncertain nonlinear under-actuated systems. Finally, simulation results show the validity of the proposed method.