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Robust fuzzy control for fractional-order systems with estimated fraction-order

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Abstract

In this paper, a fuzzy control method is proposed for a class of fractional-order chaotic systems. The dynamics of the system are unknown and are perturbed by the external disturbances. Also, the value of the fractional-order is assumed to be unknown. The type-2 fuzzy systems (T2FSs) are employed to estimate the unknown functions in the dynamics of the system. The parameters of T2FS and the value of fractional-order are estimated by unscented Kalman filter. The upper bound of the approximation error is online estimated, and a new fractional-order compensator is designed to eliminate the effect of the uncertainties and to guarantee the closed-loop stability. The effectiveness of the proposed method is shown by simulations, and the results are compared with some other techniques. It is shown that the proposed method results in better performance in the presence of unknown fractional-order and unknown perturbed dynamics.

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Change history

  • 21 October 2019

    The correct spelling of the 2nd author’s surname is Mohammadzadeh

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Acknowledgements

This paper is partly supported by the National Science Foundation of China (61473183, U1509211, 61627810), and National Key R&D Program of China (SQ2017YFGH001005).

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Authors and Affiliations

  1. Department of Automation, Shanghai Jiaotong University, Shanghai, 200240, People’s Republic of China

    Mohammad Hosein Sabzalian, Shuyi Lin & Weidong Zhang

  2. Department of Electrical Engineering, University of Bonab, Bonab, Iran

    Ardashir Mohammadzadeh

  3. School of Industrial Engineering, Purdue University, West Lafayette, IN, 47906, USA

    Shuyi Lin

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  1. Mohammad Hosein Sabzalian
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Correspondence to Weidong Zhang.

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The correct spelling of the 2nd author’s surname is Mohammadzadeh. The original version of this article was revised.

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Sabzalian, M.H., Mohammadzadeh, A., Lin, S. et al. Robust fuzzy control for fractional-order systems with estimated fraction-order. Nonlinear Dyn 98, 2375–2385 (2019). https://doi.org/10.1007/s11071-019-05217-w

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