Output tracking control for uncertain underactuated systems based on fuzzy sliding mode control approach

This paper proposes the fuzzy sliding mode control approach to deal with the output tracking of the uncertain underactuated system. It is well-known that the presence of uncertainties which include modeling error, unmodeled dynamics, external disturbances and parameter variations is a very common problem in various kinds of engineering systems. First, the whole underactuated system is divided into several different subsystems. The first-level sliding surfaces are defined for each subsystem. Hence, we further construct a second-level surface from these first-level sliding surfaces. The fuzzy logic systems and some adaptive laws are used to approximate the unknown nonlinear functions and estimate the upper bounds of the unknown disturbances, respectively. Based on Lyapunov stability theorem and the theory of sliding mode control, the proposed control scheme not only ensures the robust stability of the uncertain underactuated system but also obtains good tracking performance. Finally, a simulated example is given to show the validity of the proposed control method.