IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v152y2021ics0960077921007256.html
   My bibliography  Save this article

Optimal control for uncertain random singular systems with multiple time-delays

Author

Listed:
  • Chen, Xin
  • Zhu, Yuanguo

Abstract

Chance theory provides us a useful tool to solve an optimal control problem with indeterminacy composing of both uncertainty and randomness. Based on chance theory, this paper studies an optimal control for uncertain random singular systems with multiple time-delays. First, an uncertain random singular system with multiple time-delays is introduced, and then the corresponding optimal control problem is established. The equivalent relationship between this problem and the optimal control problem for standard uncertain random systems is derived. Then the appropriate recurrence equations are proposed according to the dynamic programming method. Furthermore, two kinds of optimal control problems are discussed. The optimal control inputs and respective optimal values of the problems are provided via the solvability of the obtained equations. Finally, a numerical example is presented to show the effectiveness of our theoretical results.

Suggested Citation

  • Chen, Xin & Zhu, Yuanguo, 2021. "Optimal control for uncertain random singular systems with multiple time-delays," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    • Handle: RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921007256
    DOI: 10.1016/j.chaos.2021.111371
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921007256
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.111371?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. Meilin Wen & Rui Kang, 2016. "Reliability analysis in uncertain random system," Fuzzy Optimization and Decision Making, Springer, vol. 15(4), pages 491-506, December.
    2. Luenberger, David G & Arbel, Ami, 1977. "Singular Dynamic Leontief Systems," Econometrica, Econometric Society, vol. 45(4), pages 991-995, May.
    3. Li, Bo & Zhang, Ranran, 2021. "A new mean-variance-entropy model for uncertain portfolio optimization with liquidity and diversification," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    4. Qin, Zhongfeng, 2015. "Mean-variance model for portfolio optimization problem in the simultaneous presence of random and uncertain returns," European Journal of Operational Research, Elsevier, vol. 245(2), pages 480-488.
    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. Jia, Zhifu & Liu, Xinsheng, 2023. "Uncertain stochastic hybrid differential game system with V-n jumps: Saddle point equilibrium strategies and application to advertising duopoly game," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    3. Nosrati, Komeil & Belikov, Juri & Tepljakov, Aleksei & Petlenkov, Eduard, 2023. "Extended fractional singular kalman filter," Applied Mathematics and Computation, Elsevier, vol. 448(C).
    4. Xu, Qinqin & Zhu, Yuanguo, 2022. "Reliability modeling of uncertain random fractional differential systems with competitive failures," Chaos, Solitons & Fractals, Elsevier, vol. 162(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. Li, Bo & Li, Xiangfa & Teo, Kok Lay & Zheng, Peiyao, 2022. "A new uncertain random portfolio optimization model for complex systems with downside risks and diversification," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    2. Jie, Ke-Wei & Liu, San-Yang & Sun, Xiao-Jun & Xu, Yun-Cheng, 2023. "A dynamic ripple-spreading algorithm for solving mean–variance of shortest path model in uncertain random networks," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    3. Wang, Dan & Qin, Zhongfeng & Kar, Samarjit, 2015. "A novel single-period inventory problem with uncertain random demand and its application," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 133-145.
    4. Dobos, Imre, 2007. "Egy megjegyzés Bródy András: Leontief zárt dinamikus modellje című dolgozathoz [A note on András Bródys study entitled Leontiefs closed dynamic model"]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(11), pages 1004-1011.
    5. Zhang, Cheng & Gong, Xiaomin & Zhang, Jingshu & Chen, Zhiwei, 2023. "Dynamic portfolio allocation for financial markets: A perspective of competitive-cum-compensatory strategy," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 84(C).
    6. Xiaoxia Huang & Xuting Wang, 2019. "Portfolio Investment with Options Based on Uncertainty Theory," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 18(03), pages 929-952, May.
    7. Wei Chen & Yuxi Gai & Pankaj Gupta, 2018. "Efficiency evaluation of fuzzy portfolio in different risk measures via DEA," Annals of Operations Research, Springer, vol. 269(1), pages 103-127, October.
    8. Gao, Rong & Zhang, Shijie, 2024. "Reliability importance analysis of uncertain random k-out-of-n systems with multiple states," Reliability Engineering and System Safety, Elsevier, vol. 243(C).
    9. Zinoviy Landsman & Udi Makov & Tomer Shushi, 2018. "A Generalized Measure for the Optimal Portfolio Selection Problem and its Explicit Solution," Risks, MDPI, vol. 6(1), pages 1-15, March.
    10. He, Yijun & Barnett, William A., 2006. "Singularity bifurcations," Journal of Macroeconomics, Elsevier, vol. 28(1), pages 5-22, March.
    11. William A. Barnett & Yijun He, 2002. "Bifurcations in Macroeconomic Models," Macroeconomics 0210006, University Library of Munich, Germany.
    12. Barnett, William A. & Chen, Guo, 2015. "Bifurcation of Macroeconometric Models and Robustness of Dynamical Inferences," Foundations and Trends(R) in Econometrics, now publishers, vol. 8(1-2), pages 1-144, September.
    13. Xin-Rong Yang & Guo-Ping Liu, 2017. "Admissible consensus for networked singular multi-agent systems with communication delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(4), pages 705-714, March.
    14. Guo, Sini & Yu, Lean & Li, Xiang & Kar, Samarjit, 2016. "Fuzzy multi-period portfolio selection with different investment horizons," European Journal of Operational Research, Elsevier, vol. 254(3), pages 1026-1035.
    15. Mingxuan Zhao & Yuhan Liu & Dan A. Ralescu & Jian Zhou, 2018. "The covariance of uncertain variables: definition and calculation formulae," Fuzzy Optimization and Decision Making, Springer, vol. 17(2), pages 211-232, June.
    16. Lifeng Wang & Jinwu Gao & Hamed Ahmadzade & Zezhou Zou, 2023. "Partial Gini Coefficient for Uncertain Random Variables with Application to Portfolio Selection," Mathematics, MDPI, vol. 11(18), pages 1-18, September.
    17. Kiran Bisht & Arun Kumar, 2022. "Stock Portfolio Selection Hybridizing Fuzzy Base-Criterion Method and Evidence Theory in Triangular Fuzzy Environment," SN Operations Research Forum, Springer, vol. 3(4), pages 1-32, December.
    18. Naomi Pandiangan & Sukono Sukono & Endang Soeryana Hasbullah, 2021. "Quadratic Investment Portfolio Based on Value-at-risk with Risk-Free Assets: For Stocks of the Mining and Energy Sector," International Journal of Energy Economics and Policy, Econjournals, vol. 11(4), pages 175-184.
    19. Yuanyuan Zhang & Xiang Li & Sini Guo, 2018. "Portfolio selection problems with Markowitz’s mean–variance framework: a review of literature," Fuzzy Optimization and Decision Making, Springer, vol. 17(2), pages 125-158, June.
    20. Biao Huang, 2018. "An exhaustible resources model in a dynamic input–output framework: a possible reconciliation between Ricardo and Hotelling," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 7(1), pages 1-24, 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:152:y:2021:i:c:s0960077921007256. 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.