Nonlinear Dynamics

, Volume 92, Issue 3, pp 1079–1089 | Cite as

Observer-based adaptive stabilization of the fractional-order chaotic MEMS resonator

  • Shaohua Luo
  • Shaobo Li
  • Farid Tajaddodianfar
  • Jianjun Hu
Original Paper


Compared to the integer-order chaotic MEMS resonator, the fractional-order system can better model its hereditary properties and exhibit complex dynamical behavior. Following the increasing attention to adaptive stabilization in controller design, this paper deals with the observer-based adaptive stabilization issue of the fractional-order chaotic MEMS resonator with uncertain function, parameter perturbation, and unmeasurable states under electrostatic excitation. To compensate the uncertainty, a Chebyshev neural network is applied to approximate the uncertain function while its weight is tuned by a parametric update law. A fractional-order state observer is then constructed to gain unmeasured feedback information and a tracking differentiator based on a super-twisting algorithm is employed to avoid repeated derivative in the framework of backstepping. Based on the Lyapunov stability criterion and the frequency-distributed model of the fractional integrator, it is proved that the adaptive stabilization scheme not only guarantees the boundedness of all signals, but also suppresses chaotic motion of the system. The effectiveness of the proposed scheme for the fractional-order chaotic MEMS resonator is illustrated through simulation studies.


Fractional-order MEMS resonator Chaos suppression Sate observer Adaptive stabilization Fractional-order backstepping 



This work is funded by the National Natural Science Foundation of China (Nos. 51505170, 51375506, 51505045, 51475097 and 51375506), Major Research Plan of National Natural Science Foundation of China (No. 91746116), Major Project of Basic Research of Guizhou Province (No. [2014]2001), Key Scientific Research Program of Guizhou Province (No. [2017]3001) and High–level Innovative Talent Program of Guizhou Province (No. [2015]4011).

Compliance with ethical standards

Conflict of interest

The authors confirm that this article content has no conflict of interest.


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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  • Shaohua Luo
    • 1
  • Shaobo Li
    • 1
    • 2
  • Farid Tajaddodianfar
    • 3
  • Jianjun Hu
    • 4
  1. 1.Key Laboratory of Advanced Manufacturing Technology, Ministry of EducationGuizhou UniversityGuiyangChina
  2. 2.School of Mechanical EngineeringGuizhou UniversityGuiyangChina
  3. 3.Department of Mechanical Engineering, Erik Jonsson School of Engineering and Computer ScienceThe University of Texas at DallasRichardsonUSA
  4. 4.Department of Computer Science and Engineering University of South CarolinaColumbiaUSA

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