Adaptive fuzzy control scheme for MIMO systems with uncertainties

Based on the Lyapunov synthesis approach and regarding the fuzzy systems as approximators to approximate the unknown functions in the system to be controlled, several adaptive fuzzy control schemes have been developed during the last decade. Actually, these schemes have been applied only to simple classes of nonlinear systems. In the concrete, (i) most of them just consider SISO systems (which can avoid the challenging of the coupling between control inputs); (ii) the upper bounds of uncertainties, and the reconstruction errors between the best approximators and their corresponding functions to be approximated are assumed to be known (in this way, the traditional adaptive methods or robust methods could be utilized straightforwardly). This paper develops a design methodology that expends the class of nonlinear systems to MIMO systems, the above restrictive assumptions can be relaxed by using an unique way to deal with the uncertainties and the reconstruction errors. The overall adaptive scheme is shown to guarantee the tracking error, between the outputs of system and the desired values, to be asymptotical in decay.