# American Institute of Mathematical Sciences

July  2022, 15(7): 1615-1631. doi: 10.3934/dcdss.2021144

## Fuzzy adaptive asymptotic tracking of fractional order nonlinear systems with uncertain disturbances

 College of Science, Liaoning University of Technology, Jinzhou, 121001, China

*Corresponding author: Yuan-Xin Li

Received  August 2021 Revised  September 2021 Published  July 2022 Early access  December 2021

Fund Project: The first author is supported part by the Funds of National Science of China (Grant Nos. 61973146, 61773188), in part by the Doctoral Research Initiation of Foundation of Liaoning Province (No. 20180540047), and in part by the Distinguished Young Scientific Research Talents Plan in Liaoning Province (Nos. XLYC1907077, JQL201915402)

In this article, an adaptive asymptotic tracking control scheme is proposed for fractional order nonlinear systems (FONSs) with time-varying disturbance. By introducing some well defined smooth functions and the bounded estimation approach, the effects caused by the unknown virtual control coefficients (UVCC) and unknown nonlinear functions are counteracted. For the UVCC, we only need to assume that their lower bounds are positive constants. Fuzzy logic systems (FLSs) are applied to approximate unknown nonlinear functions. Moreover, the fractional directed Lyapunov method is used to prove that the tracking error asymptotically converges to zero. Finally, an illustrative simulation example is applied to verify the superior performance of the presented control algorithms.

Citation: Jin-Zi Yang, Yuan-Xin Li, Ming Wei. Fuzzy adaptive asymptotic tracking of fractional order nonlinear systems with uncertain disturbances. Discrete and Continuous Dynamical Systems - S, 2022, 15 (7) : 1615-1631. doi: 10.3934/dcdss.2021144
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##### References:
Trajectories of $y$ and $y_{r}$
State trajectories of $x_1$ and $x_2$
Control input
Tracking error $z_1$
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