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Backstepping-Based Finite-Time Adaptive Fuzzy Control of Unknown Nonlinear Systems

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Abstract

This paper proposes a backstepping-based finite-time adaptive fuzzy controller (BFAFC) for a nonlinear system in the present of unknown and uncertainty terms. A nonsingleton type-2 fuzzy system is presented to online approximate the unknown term in the nonlinear system, where the ellipsoidal type-2 membership functions are considered to deal with large amounts of uncertainties. Moreover, to further improve the control performance, the parameter adaptive laws are designed by the Lyapunov function and finite-time stability theorem in this paper such that not only the system stability but also the finite-time convergence can be guaranteed. Finally, the proposed BFAFC system is applied to an inverted pendulum and a coupled chaotic system to validate the effectiveness of the BFAFC system. Simulation results show that the proposed BFAFC system can cause the tracking error to converge to zero in a finite time and the tracking accuracy can be improved satisfactorily.

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Acknowledgements

The authors appreciate the partial financial support from the Ministry of Science and Technology of Republic of China under Grant MOST 105-2628-E-032-001-MY3.

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Authors and Affiliations

  1. Department of Information and Telecommunications Engineering, Ming Chuan University, Taipei, Taiwan

    Chia-Wen Chang

  2. Department of Electrical Engineering, Tamkang University, New Taipei City, Taiwan

    Chun-Fei Hsu & Tsu-Tian Lee

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  1. Chia-Wen Chang
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  3. Tsu-Tian Lee
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Correspondence to Chun-Fei Hsu.

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Chang, CW., Hsu, CF. & Lee, TT. Backstepping-Based Finite-Time Adaptive Fuzzy Control of Unknown Nonlinear Systems. Int. J. Fuzzy Syst. 20, 2545–2555 (2018). https://doi.org/10.1007/s40815-018-0505-4

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  • DOI: https://doi.org/10.1007/s40815-018-0505-4

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