Tracking Control of the Nolinear System with Hysteresis Nonlinearity via the Variable Universe Fuzzy H∞ Controller

In this paper, a novel control scheme based on the variable universe fuzzy control and H-infinity control for improving the robustness of the designed controller is developed for a class of nonlinear systems preceded by the hysteresis nonlinearity. The controller guarantees the boundedness of all variables in the close-loop systems and convergence of the plant output to a given reference signal. To design the controller, we show that the implicit function - the composite function of system nonlinearities and hysteresis, has a unique solution which yields the convergence of the tracking error to the zero. Therefore, instead of necessarily constructing or approximating a hysteresis inverse as done in the inverse compensation, the proposed controller is constructed to approximate the unique solution of the implicit function. Finally, simulation example is presented to demonstrate the electiveness of the proposed approach.