Design of adaptive fuzzy controller for uncertain fuzzy systems with multiple time delays

In this paper, an adaptive fuzzy control scheme for fuzzy systems with multiple delayed state perturbations, timevarying uncertain parameters, and disturbances. These delayed state perturbations, uncertainties, and external disturbances in the fuzzy systems are assumed to be any uncertain bounded but unknown continuous functions. An improved adaptation law with σ-modification is proposed to estimate such unknown bounds, and on the basis of the updated values of these unknown bounds, a continuous memoryless state feedback controller is constructed for achieving robust stability of the closed-loop system. Based on Lyapunov stability theorem, the proposed adaptive robust fuzzy controller can guarantee that the state converges asymptotically to zero in the presence of multiple delayed state perturbations, time-varying uncertain parameters, and disturbance. In addition, it is also shown that this improved adaptation law with σ-modification can be applied to the general adaptive control problems to obtain some more exact control results. Finally, an inverted pendulum system is given to demonstrate the validity of the proposed design method.