Control of a class of under-actuated systems with saturation using hierarchical sliding mode

This paper presents a control scheme of a class of under-actuated systems with saturation using hierarchical sliding mode. This class with a single input and multiple outputs is made up of several subsystems. Based on this physical structure, the hierarchical structure of the sliding mode surfaces is developed as follows. The sliding surface of every subsystem is defined. Then the sliding surface of one subsystem is selected 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 all the subsystem sliding surfaces are included. The hierarchical sliding mode control law is deduced by using Lyapunov theorem. On account of saturation nonlinearity of the single input, asymptotic stability of the control system is proven by nonlinear small gain theorem. Parameter ranges of the subsystem sliding surfaces are also given. In practice, simulation and experimental results show the validity of this control method.