IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v147y2021ics0960077921003386.html
   My bibliography  Save this article

LQ optimal control of fractional-order discrete-time uncertain systems

Author

Listed:
  • Lu, Qinyun
  • Zhu, Yuanguo

Abstract

This paper primarily focuses on LQ optimal control problem of fractional-order discrete-time systems based on uncertainty theory that is a significant tool to model belief degree. First, an equivalent LQ problem, which is integer-order one, is presented by expanding the state variables with the unchanging control variables. This equivalent problem is then solved by dynamic programming approach. Accordingly, the solution of the proposed LQ optimal control problem reduces to solve a system of backward matrix difference equations. Finally, a numerical example is provided to show how to solve the proposed LQ optimal control problem. As an application, an LQ optimal control problem of macroeconomic system is discussed by the achieved results.

Suggested Citation

  • Lu, Qinyun & Zhu, Yuanguo, 2021. "LQ optimal control of fractional-order discrete-time uncertain systems," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    • Handle: RePEc:eee:chsofr:v:147:y:2021:i:c:s0960077921003386
    DOI: 10.1016/j.chaos.2021.110984
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921003386
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.110984?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. Lu, Ziqiang & Zhu, Yuanguo, 2019. "Numerical approach for solution to an uncertain fractional differential equation," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 137-148.
    2. Lu, Ziqiang & Zhu, Yuanguo & Li, Bo, 2019. "Critical value-based Asian option pricing model for uncertain financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 694-703.
    3. Škovránek, Tomáš & Podlubny, Igor & Petráš, Ivo, 2012. "Modeling of the national economies in state-space: A fractional calculus approach," Economic Modelling, Elsevier, vol. 29(4), pages 1322-1327.
    4. Jin, Ting & Zhu, Yuanguo, 2020. "First hitting time about solution for an uncertain fractional differential equation and application to an uncertain risk index model," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    5. Zhenhua Hu & Wen Chen, 2013. "Modeling of Macroeconomics by a Novel Discrete Nonlinear Fractional Dynamical System," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-9, December.
    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. Shen, Jiayu & Shi, Jianxin & Gao, Lingceng & Zhang, Qiang & Zhu, Kai, 2023. "Uncertain green product supply chain with government intervention," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 136-156.
    2. Danca, Marius-F., 2022. "Fractional order logistic map: Numerical approach," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).

    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. Weiwei Wang & Dan A. Ralescu, 2021. "Option pricing formulas based on uncertain fractional differential equation," Fuzzy Optimization and Decision Making, Springer, vol. 20(4), pages 471-495, December.
    2. Wang, Jian & Zhu, Yuanguo & Gu, Yajing & Lu, Ziqiang, 2021. "Solutions of linear uncertain fractional order neutral differential equations," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    3. Jin, Ting & Yang, Xiangfeng, 2021. "Monotonicity theorem for the uncertain fractional differential equation and application to uncertain financial market," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 203-221.
    4. Liu, Yiyu & Zhu, Yuanguo & Lu, Ziqiang, 2021. "On Caputo-Hadamard uncertain fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    5. Jin, Ting & Ding, Hui & Xia, Hongxuan & Bao, Jinfeng, 2021. "Reliability index and Asian barrier option pricing formulas of the uncertain fractional first-hitting time model with Caputo type," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    6. Jin, Ting & Sun, Yun & Zhu, Yuanguo, 2020. "Time integral about solution of an uncertain fractional order differential equation and application to zero-coupon bond model," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    7. He, Liu & Zhu, Yuanguo, 2024. "Nonparametric estimation for uncertain fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    8. Liu He & Yuanguo Zhu & Ziqiang Lu, 2023. "Parameter estimation for uncertain fractional differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 22(1), pages 103-122, March.
    9. Jin, Ting & Zhu, Yuanguo, 2020. "First hitting time about solution for an uncertain fractional differential equation and application to an uncertain risk index model," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    10. Yüzbaşı, Şuayip & Yıldırım, Gamze, 2022. "A collocation method to solve the parabolic-type partial integro-differential equations via Pell–Lucas polynomials," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    11. Caiwen Gao & Zhiqiang Zhang & Baoliang Liu, 2022. "Uncertain Population Model with Jumps," Mathematics, MDPI, vol. 10(13), pages 1-12, June.
    12. Zhiwei Wang & Yuanguo Zhu, 2024. "LQ optimal control of uncertain fractional differential systems," Fuzzy Optimization and Decision Making, Springer, vol. 23(4), pages 577-597, December.
    13. Ali Balcı, Mehmet, 2017. "Time fractional capital-induced labor migration model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 477(C), pages 91-98.
    14. Michal Fečkan & JinRong Wang, 2017. "Mixed Order Fractional Differential Equations," Mathematics, MDPI, vol. 5(4), pages 1-9, November.
    15. Valentina V. Tarasova & Vasily E. Tarasov, 2017. "Logistic map with memory from economic model," Papers 1712.09092, arXiv.org.
    16. Llibre, Jaume & Valls, Clàudia, 2018. "On the global dynamics of a finance model," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 1-4.
    17. Hao Ming & JinRong Wang & Michal Fečkan, 2019. "The Application of Fractional Calculus in Chinese Economic Growth Models," Mathematics, MDPI, vol. 7(8), pages 1-6, July.
    18. Svenkeson, A. & Beig, M.T. & Turalska, M. & West, B.J. & Grigolini, P., 2013. "Fractional trajectories: Decorrelation versus friction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(22), pages 5663-5672.
    19. Jia, Lifen & Chen, Wei, 2020. "Knock-in options of an uncertain stock model with floating interest rate," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    20. Benito Chen-Charpentier & Gilberto González-Parra & Abraham J. Arenas, 2016. "Fractional Order Financial Models for Awareness and Trial Advertising Decisions," Computational Economics, Springer;Society for Computational Economics, vol. 48(4), pages 555-568, 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:eee:chsofr:v:147:y:2021:i:c:s0960077921003386. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.