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

Yeguo Sun, Yihong Liu, Ling Li, Ahmed Mostafa Khalil
2020 Journal of Mathematics  
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
more » ... as, 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.
doi:10.1155/2020/6677704 fatcat:gu357kuhfzepvk42mkm352wh2q