Uniformly ultimately bounded uncertain adaptive tracking control 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 ify the effect of uncertainties and achieve a desired tracking performance. The interactions between the two components have been investigated. The tracking error of the closed-loop system driven by the proposed controllers is shown to be uniformly ultimately bounded with all the adaptation parameters being bounded. 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.