Fuzzy Adaptive Control for Fractional Nonlinear Systems with External Disturbances and Unknown Control Directions

Yeguo Sun, Yihong Liu, Ling Li and Ahmed Mostafa Khalil

Journal of Mathematics, 2020, vol. 2020, 1-9

Abstract: In this paper, the problem of fuzzy adaptive control of unknown nonlinear fractional-order systems with external disturbances and unknown control directions is studied. 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 novel fuzzy adaptive controller is designed. The proposed method can guarantee that all the signals in the closed-loop systems remain bounded and the tracking errors converge to an arbitrary small region of the origin. In addition, 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.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:6677704

DOI: 10.1155/2020/6677704

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