Uniformly ultimately bounded fuzzy adaptive tracking controllers for uncertain systems

Fuzzy adaptive tracking controllers for a class of uncertain nonlinear dynamical systems are proposed and analyzed. The controllers consist of adaptive and robustifying components whose role is to nullify the effects of uncertainties and to achieve a desired tracking performance. The interactions between the two components have been investigated. The closed-loop system driven by the proposed controllers is shown to be stable with all the adaptation parameters being bounded. In particular, the proposed controllers guarantee uniform ultimate boundedness of the tracking error and the time bound of the uniform ultimate boundedness is obtained. An upper bound on the steady-state tracking error is obtained as a function of the gain of the robustifying term and the parameters of the adaptive component. The controllers are tested on an inverted pendulum and simulation results are included. A comparison of the proposed controllers with the ones in the literature is conducted.