Adaptive fuzzy output-feedback dynamic surface control of MIMO switched nonlinear systems with unknown gain signs

This paper investigates the problem of adaptive fuzzy tracking control for a class of multi-input-multi-output (MIMO) switched uncertain nonlinear systems with unknown gain signs and unmeasurable states. Fuzzy logic systems are used to approximate the unknown nonlinear functions, a fuzzy MIMO switched observer is designed to estimate the unmeasurable states. The Nussbaum-type functions are utilized to handle the unknown gain signs of the system under study. A switched-dynamic-surface-based adaptive fuzzy control approach is then established by exploiting the average dwell time method and backstepping and the dynamic surface control technique, which constructs multiple switched first-order filters to overcome the multiple “explosion of complexity” problem when applying the backstepping recursive design scheme. Also, the proposed approach extends the classical dynamic surface control technique from its original non-switched nonlinear version to a switched nonlinear version. It is proved that all the signals in the closed-loop system are semiglobal uniformly ultimately boundedness under a class of switching signals with average dwell time, and the tracking errors converge to a small neighborhood of the origin. A mass-spring-damper system with controller switching as a practical example is provided to demonstrate the effectiveness of the proposed design method.