Adaptive fuzzy H∞ tracking design of SISO uncertain nonlinear fractional order time-delay systems

In this paper, a fuzzy logic controller equipped with training algorithms is developed such that the H∞ tracking performance should be satisfied for a model-free nonlinear fractional order time delay system which is infinite dimensional in nature and time delay is a source of instability. In order to deal with the linguistic uncertainties caused from delay terms, the adaptive time delay fuzzy logic system is constructed to approximate the unknown time delay system functions. By incorporating Lyapunov stability criterion with H∞ tracking design technique, the free parameters of the adaptive fuzzy controller can be tuned on line by output feedback control law and adaptive law. Moreover, the tracking error and external disturbance can be attenuated to arbitrary desired level. The numerical results show the effectiveness of the proposed adaptive H∞ tracking scheme.