International Journal of Fuzzy Systems

, Volume 20, Issue 8, pp 2545–2555 | Cite as

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

  • Chia-Wen Chang
  • Chun-Fei Hsu
  • Tsu-Tian Lee


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.


Adaptive control Backstepping control Finite-time stability Ellipsoidal type-2 membership function 



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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Copyright information

© Taiwan Fuzzy Systems Association and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Information and Telecommunications EngineeringMing Chuan UniversityTaipeiTaiwan
  2. 2.Department of Electrical EngineeringTamkang UniversityNew Taipei CityTaiwan

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