Observer-based fuzzy adaptive H∞ tracking control for nonlinear time-delay systems

In this paper, an observer-based fuzzy sliding mode adaptive control design algorithm with H tracking performance is presented for a class of nonlinear SISO delayed systems. To facilitate this concept, an observer is developed for the error dynamics and Lyapunov type stability is established under certain condition. The fuzzy approximators equipped with adaptive algorithms are introduced to learn the behaviors of the uncertain dynamics. It is shown that all the states and signals of the system are bounded and the effect of the external disturbance on the tracking error can be attenuated to any prescribed level and consequently an H-infinity tracking performance is achieved. Finally, simulation examples by the application to control of a car-like inverted pendulum are included to confirm the validity and performance of the proposed algorithm.