Multiple Layers Sliding Mode Control for a Class of Under-actuated Systems

This paper presents a multiple layers sliding mode controller for a class of under-actuated systems. The structure characteristic of these systems, such as inverted pendulum(s) systems, is that they are made up of several subsystems. Firstly, the given system is divided into several subsystems. Then, one subsystem is selected to construct the first layer sliding mode surface and it is used to construct the second layer sliding mode surface with the sliding mode surface of another subsystem. This process continues till all states of all subsystems are included. The controller is designed according to this multiple layers structure. The asymptotic stability of the entire sliding mode surfaces is proved theoretically. Simulation results show the validity of this method with limited control force