IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v197y2023i3d10.1007_s10957-023-02220-5.html
   My bibliography  Save this article

Stochastic $$H_{2}/H_{\infty }$$ H 2 / H ∞ Control for Mean-Field Stochastic Differential Systems with (x, u, v)-Dependent Noise

Author

Listed:
  • Meijiao Wang

    (University of Shanghai for Science and Technology)

  • Qingxin Meng

    (Huzhou University)

  • Yang Shen

    (University of New South Wales)

  • Peng Shi

    (The University of Adelaide)

Abstract

This paper studies a continuous-time stochastic $$H_{2}/H_{\infty }$$ H 2 / H ∞ control problem for mean-field stochastic differential systems, with random initial value and diffusion coefficients depending explicitly on the state, control and disturbance as well as their expectations. A mean-field stochastic bounded real lemma is first established, characterizing the equivalence between $$H_{\infty }$$ H ∞ robust stability and the solvability of two indefinite differential Riccati equations. Based on this extremely useful result, an equivalent condition for the existence of $$H_{2}/H_{\infty }$$ H 2 / H ∞ controller is proposed by utilizing the solution of two sets of cross-coupled indefinite Riccati equations. Moreover, when an $$H_{2}/H_{\infty }$$ H 2 / H ∞ controller exists, both the optimal control input and the corresponding worst-case disturbance admit linear feedback representations of the state and its mathematical expectation.

Suggested Citation

  • Meijiao Wang & Qingxin Meng & Yang Shen & Peng Shi, 2023. "Stochastic $$H_{2}/H_{\infty }$$ H 2 / H ∞ Control for Mean-Field Stochastic Differential Systems with (x, u, v)-Dependent Noise," Journal of Optimization Theory and Applications, Springer, vol. 197(3), pages 1024-1060, June.
    • Handle: RePEc:spr:joptap:v:197:y:2023:i:3:d:10.1007_s10957-023-02220-5
    DOI: 10.1007/s10957-023-02220-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-023-02220-5
    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/s10957-023-02220-5?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. Rodrigo da Ponte Caun & Edvaldo Assunção & Marcelo Carvalho Minhoto Teixeira, 2021. "H2/H∞ formulation of LQR controls based on LMI for continuous-time uncertain systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 52(3), pages 612-634, February.
    2. Buckdahn, Rainer & Li, Juan & Peng, Shige, 2009. "Mean-field backward stochastic differential equations and related partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3133-3154, October.
    Full references (including those not matched with items on IDEAS)

    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. Qun Shi, 2021. "Generalized Mean-Field Fractional BSDEs With Non-Lipschitz Coefficients," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(3), pages 1-77, June.
    2. Kaitong Hu & Zhenjie Ren & Junjian Yang, 2019. "Principal-agent problem with multiple principals," Working Papers hal-02088486, HAL.
    3. Kamal Boukhetala & Jean-François Dupuy, 2019. "Modélisation Stochastique et Statistique Book of Proceedings," Post-Print hal-02593238, HAL.
    4. Douissi, Soukaina & Wen, Jiaqiang & Shi, Yufeng, 2019. "Mean-field anticipated BSDEs driven by fractional Brownian motion and related stochastic control problem," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 282-298.
    5. Bender, Christian, 2014. "Backward SDEs driven by Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 124(9), pages 2892-2916.
    6. Salah Eddine Choutri & Tembine Hamidou, 2018. "A Stochastic Maximum Principle for Markov Chains of Mean-Field Type," Games, MDPI, vol. 9(4), pages 1-21, October.
    7. Fu, Guanxing & Horst, Ulrich & Xia, Xiaonyu, 2022. "Portfolio Liquidation Games with Self-Exciting Order Flow," Rationality and Competition Discussion Paper Series 327, CRC TRR 190 Rationality and Competition.
    8. Wu, Zhen & Xu, Ruimin, 2019. "Probabilistic interpretation for Sobolev solutions of McKean–Vlasov partial differential equations," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 273-283.
    9. Sin, Myong-Guk & Ri, Kyong-Il & Kim, Kyong-Hui, 2022. "Existence and uniqueness of solution for coupled fractional mean-field forward–backward stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 190(C).
    10. Romuald Elie & Thibaut Mastrolia & Dylan Possamaï, 2019. "A Tale of a Principal and Many, Many Agents," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 440-467, May.
    11. Klimsiak, Tomasz & Rzymowski, Maurycy, 2023. "Nonlinear BSDEs on a general filtration with drivers depending on the martingale part of the solution," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 424-450.
    12. Briand, Philippe & Cardaliaguet, Pierre & Chaudru de Raynal, Paul-Éric & Hu, Ying, 2020. "Forward and backward stochastic differential equations with normal constraints in law," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7021-7097.
    13. Cai, Yujie & Huang, Jianhui & Maroulas, Vasileios, 2015. "Large deviations of mean-field stochastic differential equations with jumps," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 1-9.
    14. Boualem Djehiche & Hamidou Tembine, 2014. "Risk-Sensitive Mean-Field Type Control under Partial Observation," Papers 1411.7231, arXiv.org.
    15. Aurell, Alexander & Djehiche, Boualem, 2019. "Modeling tagged pedestrian motion: A mean-field type game approach," Transportation Research Part B: Methodological, Elsevier, vol. 121(C), pages 168-183.
    16. Zong, Gaofeng & Chen, Zengjing, 2013. "Harnack inequality for mean-field stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1424-1432.
    17. Pei Zhang & Nur Anisah Mohamed & Adriana Irawati Nur Ibrahim, 2023. "Mean-Field and Anticipated BSDEs with Time-Delayed Generator," Mathematics, MDPI, vol. 11(4), pages 1-13, February.
    18. Lu, Wen & Ren, Yong & Hu, Lanying, 2015. "Mean-field backward stochastic differential equations with subdifferential operator and its applications," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 73-81.
    19. Chaudru de Raynal, P.E. & Garcia Trillos, C.A., 2015. "A cubature based algorithm to solve decoupled McKean–Vlasov forward–backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 125(6), pages 2206-2255.
    20. Buckdahn, Rainer & Chen, Yajie & Li, Juan, 2021. "Partial derivative with respect to the measure and its application to general controlled mean-field systems," Stochastic Processes and their Applications, Elsevier, vol. 134(C), pages 265-307.

    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:197:y:2023:i:3:d:10.1007_s10957-023-02220-5. 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.