Decoupled fuzzy adaptive sliding mode control for under-actuated systems with mismatched uncertainties

This paper presents a decoupled sliding mode controller with fuzzy logic adaptive tuner for a class of under actuated systems with mismatched uncertainties. By using the concept of hierarchical decoupling method, the coupled nonlinear system can be decoupled into several subsystems. Each subsystem has a separate control target expressed in terms of a sliding surface. From sliding surface of subsystems, we can organize a sliding surface which includes all sliding surfaces for each sub systems. To design control law, adaptive fuzzy inference scheme is used to approximate the unknown coupling factors. With Lyapunov stability theory and barbalat´s lemma, the entire closed loop system is proved to be stable and convergence properties of the system is assured. Simulation results have shown the validity of the proposed approach and its robustness for uncertainties.