Fuzzy Incremental Hierarchical Sliding Mode Control for Underactuated Systems

This paper designs a fuzzy incremental hierarchical sliding mode controller for a class of under actuated systems. By capturing the physical structure of the class, the hierarchical sliding surfaces with incremental structure are designed as follows. The first-layer sliding surface is firstly defined. Then, the first-layer sliding surface and one of the left states are employed to construct the second-layer sliding surface. The process continues till all the state variables are included. The control law is deduced from Lyapunov stability scheme. For decreasing the chattering phenomenon of the sliding mode, a fuzzy regulator is presented to regulate the controller gain. Simulation results illustrate the feasibility of the present method.