IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v187y2020i1d10.1007_s10957-017-1163-7.html
   My bibliography  Save this article

A Control Parameterization Method to Solve the Fractional-Order Optimal Control Problem

Author

Listed:
  • Pan Mu

    (Dalian University of Technology)

  • Lei Wang

    (Dalian University of Technology)

  • Chongyang Liu

    (Shandong Institute of Business and Technology
    Curtin University)

Abstract

This paper considers a class of fractional optimal control problems with canonical equality and inequality constraints. A fractional derivative in the dynamic system is defined in the Caputo sense. Using the control parameterization method, we approximate fractional optimal control problems by a sequence of finite-dimensional optimization problems. We then present the gradient formulae by introducing some auxiliary fractional systems. On this basis, a gradient-based optimization is developed to solve the fractional optimal control problems. Finally, a numerical example is used to test the proposed method.

Suggested Citation

  • Pan Mu & Lei Wang & Chongyang Liu, 2020. "A Control Parameterization Method to Solve the Fractional-Order Optimal Control Problem," Journal of Optimization Theory and Applications, Springer, vol. 187(1), pages 234-247, October.
  • Handle: RePEc:spr:joptap:v:187:y:2020:i:1:d:10.1007_s10957-017-1163-7
    DOI: 10.1007/s10957-017-1163-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-017-1163-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10957-017-1163-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ricardo Enrique Gutiérrez & João Maurício Rosário & José Tenreiro Machado, 2010. "Fractional Order Calculus: Basic Concepts and Engineering Applications," Mathematical Problems in Engineering, Hindawi, vol. 2010, pages 1-19, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Marzban, Hamid Reza, 2022. "A generalization of Müntz-Legendre polynomials and its implementation in optimal control of nonlinear fractional delay systems," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    2. Chongyang Liu & Changjun Yu & Zhaohua Gong & Huey Tyng Cheong & Kok Lay Teo, 2023. "Numerical Computation of Optimal Control Problems with Atangana–Baleanu Fractional Derivatives," Journal of Optimization Theory and Applications, Springer, vol. 197(2), pages 798-816, May.
    3. Gong, Zhaohua & Liu, Chongyang & Teo, Kok Lay & Yi, Xiaopeng, 2022. "Optimal control of nonlinear fractional systems with multiple pantograph‐delays," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    4. Gong, Zhaohua & Liu, Chongyang & Teo, Kok Lay & Wang, Song & Wu, Yonghong, 2021. "Numerical solution of free final time fractional optimal control problems," Applied Mathematics and Computation, Elsevier, vol. 405(C).
    5. Li, Bo & Huang, Tian, 2024. "Stochastic optimal control and piecewise parameterization and optimization method for inventory control system improvement," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    6. Chongyang Liu & Zhaohua Gong & Kok Lay Teo & Song Wang, 2022. "Optimal Control of Nonlinear Fractional-Order Systems with Multiple Time-Varying Delays," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 856-876, June.
    7. Chongyang Liu & Zhaohua Gong & Changjun Yu & Song Wang & Kok Lay Teo, 2021. "Optimal Control Computation for Nonlinear Fractional Time-Delay Systems with State Inequality Constraints," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 83-117, October.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fiuzy, Mohammad & Shamaghdari, Saeed, 2023. "Robust H∞-PID control Stability of fractional-order linear systems with Polytopic and two-norm bounded uncertainties subject to input saturation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 550-581.
    2. Asmae Tajani & Fatima-Zahrae El Alaoui, 2023. "Boundary Controllability of Riemann–Liouville Fractional Semilinear Evolution Systems," Journal of Optimization Theory and Applications, Springer, vol. 198(2), pages 767-780, August.
    3. Wang, Yujie & Li, Mince & Chen, Zonghai, 2020. "Experimental study of fractional-order models for lithium-ion battery and ultra-capacitor: Modeling, system identification, and validation," Applied Energy, Elsevier, vol. 278(C).
    4. Gayathri Vivekanandan & Mahtab Mehrabbeik & Hayder Natiq & Karthikeyan Rajagopal & Esteban Tlelo-Cuautle, 2022. "Fractional-Order Memristive Wilson Neuron Model: Dynamical Analysis and Synchronization Patterns," Mathematics, MDPI, vol. 10(16), pages 1-9, August.
    5. Eva-Henrietta Dulf, 2019. "Simplified Fractional Order Controller Design Algorithm," Mathematics, MDPI, vol. 7(12), pages 1-21, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:187:y:2020:i:1:d:10.1007_s10957-017-1163-7. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.