Adaptive fuzzy control for a class of nonlinear fractional-order systems

In this paper, the problem of fuzzy adaptive control of unknown nonlinear fractional-order systems with unknown control direction and external disturbance is investigated. We exploit a decomposition of the control gain matrix into a symmetric positive-definite matrix, a diagonal matrix with diagonal entries +1 or 1 and a unity upper triangular matrix. Fuzzy logic systems are used for estimating the unknown nonlinear functions. Based on the fractional Lyapunov direct method and some proposed Lemmas, a fuzzy adaptive controller is designed. The proposed method can guarantee all the signals in the closed-loop systems remain bounded and the tracking errors converge to an arbitrary small region of the origin. For updating the parameters of the fuzzy system. fractional-order adaptations laws are proposed. Lastly, an illustrative example is given to demonstrate the effectiveness of the proposed results.