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Fractional Order Systems Time-Optimal Control and Its Application

Author

Listed:
  • Yiheng Wei

    (University of Science and Technology of China)

  • Bin Du

    (University of Science and Technology of China)

  • Songsong Cheng

    (University of Science and Technology of China)

  • Yong Wang

    (University of Science and Technology of China)

Abstract

This paper deals with the time-optimal control problem for a class of fractional order systems. An analytic solution of the time-optimal problem is proposed, and the optimal transfer route is provided. Considering it is usually adopted in the discrete situation for actual control system, the sampling date may induce chattering phenomenon, an alternative sub-optimal solution is constructed. Additionally, the special and meaningful application of fractional order tracking differentiator is introduced to explain our main results. The effectiveness and advantages of the proposed method have been illustrated by numerical examples.

Suggested Citation

  • Yiheng Wei & Bin Du & Songsong Cheng & Yong Wang, 2017. "Fractional Order Systems Time-Optimal Control and Its Application," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 122-138, July.
    • Handle: RePEc:spr:joptap:v:174:y:2017:i:1:d:10.1007_s10957-015-0851-4
    DOI: 10.1007/s10957-015-0851-4
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    References listed on IDEAS

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    1. K. Balachandran & V. Govindaraj & L. Rodríguez-Germa & J. J. Trujillo, 2013. "Controllability Results for Nonlinear Fractional-Order Dynamical Systems," Journal of Optimization Theory and Applications, Springer, vol. 156(1), pages 33-44, January.
    2. Yan Li & YangQuan Chen & Hyo-Sung Ahn & Guohui Tian, 2013. "A Survey on Fractional-Order Iterative Learning Control," Journal of Optimization Theory and Applications, Springer, vol. 156(1), pages 127-140, January.
    3. Abolhassan Razminia & Dumitru Baleanu & Vahid Johari Majd, 2013. "Conditional Optimization Problems: Fractional Order Case," Journal of Optimization Theory and Applications, Springer, vol. 156(1), pages 45-55, January.
    4. R. Caponetto & G. Dongola & F. Pappalardo & V. Tomasello, 2013. "Auto-Tuning and Fractional Order Controller Implementation on Hardware in the Loop System," Journal of Optimization Theory and Applications, Springer, vol. 156(1), pages 141-152, January.
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