Hierarchical sliding mode control for a class of SIMO under-actuated systems

A hierarchical sliding mode control approach is proposed for a class of SIMO under-actuated systems. This class of under-actuated systems is made up of several subsystems. Based on this physical structure, the hierarchical structure of the sliding surfaces is designed as follows. At first, the sliding surface of every subsystem is defined. Then the sliding surface of one subsystem is defined as the first layer sliding surface. The first layer sliding surface is used to construct the second layer sliding surface with the sliding surface of another subsystem. This process continues till the sliding surfaces of the entire subsystems are included. According to the hierarchical structure, the total control law is deduced by the Lyapunov theorem. In theory, the asymptotic stability of the entire system of sliding surfaces is proven and the parameter boundaries of the subsystem sliding surfaces are given. Simulation results show the feasibility of this control method through two typical SIMO under-actuated systems.