Tracking-Error-Based Universal Adaptive Fuzzy Control for Output Tracking of Nonlinear Systems with Completely Unknown Dynamics

Abstract

In this paper, an universal adaptive fuzzy control (UAFC) scheme using output tracking error is proposed for practical tracking control of a class of nonlinear systems with unmeasured states and completely unknown perturbed dynamics including unknown dynamics and/or external disturbances. A tracking error system with measurable output is first derived from the output tracking problem, and unmeasured states are observed by an universal fuzzy state observer (UFSO), whereby adaptive fuzzy approximators and an universal adaptive gain are employed to estimate unknown dynamics and dominant unknown residuals, respectively. In conjunction with the rescaled UFSO and observation errors, the UAFC using output tracking error feedback is explicitly constructed, in a recursive manner, by employing the command filtered backstepping technique, whereby intermediate virtual signals and their first derivatives associated with complex dynamics can be reconstructed by second-order filters. Furthermore, adaptive mechanisms for fuzzy approximators and the universal gain pertaining to the UFSO and UAFC are derived from the Lyapunov synthesis. Theoretical analysis proves that all signals of the closed-loop system are bounded and the output tracking error and observation error can converge to an arbitrarily small region determined by a prescribed accuracy. Simulation results demonstrate the effectiveness and superiority of the proposed UAFC scheme.