IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v392y2021ics009630032030669x.html
   My bibliography  Save this article

H∞ control for Poisson-driven stochastic systems

Author

Listed:
  • Song, Bo
  • Zhang, Ya
  • Park, Ju H.

Abstract

The paper aims to investigate the H∞ control problem for systems perturbed by jump random noise, i.e., Poisson-driven stochastic systems (SSs). Firstly, this paper uses the Doob-Meyer decomposition and measure theory to give a model transformation method, and Poisson-driven SSs, which are SSs driven by semi-martingale, are transformed into SSs driven by compensated Poisson process. Since SSs driven by compensated Poisson process are SSs driven by martingale, we can use effective properties and tools in martingale theory to investigate the H∞ control problem. Secondly, this paper utilizes martingale theory to deal with the jump item and the sum of stochastic integrals (SIs) with respect to (w.r.t.) the continuous part of states in Itô formula, and then gives an equivalent Itô formula for SDEs driven by compensated Poisson process. Thirdly, on the basis of these, this paper presents a simple H∞ controller design method. Furthermore, the design criterion contains information about the average number of jump random events in a unit time, and one can utilize convex optimization algorithm to estimate the maximum average number of jump random events in a unit time, which the closed-loop system can tolerate to achieve the stability and H∞ performance. Finally, the usefulness of the design result is verified by two numerical examples.

Suggested Citation

  • Song, Bo & Zhang, Ya & Park, Ju H., 2021. "H∞ control for Poisson-driven stochastic systems," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    • Handle: RePEc:eee:apmaco:v:392:y:2021:i:c:s009630032030669x
    DOI: 10.1016/j.amc.2020.125716
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S009630032030669X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2020.125716?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. Aghion, Philippe & Howitt, Peter, 1992. "A Model of Growth through Creative Destruction," Econometrica, Econometric Society, vol. 60(2), pages 323-351, March.
    2. Xu, Yong & Pei, Bin & Guo, Guobin, 2015. "Existence and stability of solutions to non-Lipschitz stochastic differential equations driven by Lévy noise," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 398-409.
    3. Kang, Ting & Li, Qiang & Zhang, Qimin, 2019. "Numerical analysis of the balanced implicit method for stochastic age-dependent capital system with poisson jumps," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 166-177.
    4. Yan, Zhiguo & Park, Ju H. & Zhang, Weihai, 2018. "A unified framework for asymptotic and transient behavior of linear stochastic systems," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 31-40.
    5. Gao, Rong, 2019. "Stability in mean for uncertain differential equation with jumps," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 15-22.
    6. Steger, Thomas M., 2005. "Stochastic growth under Wiener and Poisson uncertainty," Economics Letters, Elsevier, vol. 86(3), pages 311-316, March.
    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. Lafforgue, Gilles, 2008. "Stochastic technical change, non-renewable resource and optimal sustainable growth," Resource and Energy Economics, Elsevier, vol. 30(4), pages 540-554, December.
    2. Tsuboi, Mizuki, 2019. "Resource scarcity, technological progress, and stochastic growth," Economic Modelling, Elsevier, vol. 81(C), pages 73-88.
    3. Ken Sennewald & Klaus Wälde, 2006. "“Itô's Lemma” and the Bellman Equation for Poisson Processes: An Applied View," Journal of Economics, Springer, vol. 89(1), pages 1-36, October.
    4. Mizuki Tsuboi, 2018. "Stochastic accumulation of human capital and welfare in the Uzawa–Lucas model: an analytical characterization," Journal of Economics, Springer, vol. 125(3), pages 239-261, November.
    5. Sennewald, Ken & Wälde, Klaus, 2005. ""Itô's Lemma" and the Bellman equation: An applied view," Dresden Discussion Paper Series in Economics 04/05, Technische Universität Dresden, Faculty of Business and Economics, Department of Economics.
    6. Motoh Tsujimura & Hidekazu Yoshioka, 2023. "A robust consumption model when the intensity of technological progress is ambiguous," Mathematics and Financial Economics, Springer, volume 17, number 2, June.
    7. Song, Bo & Zhang, Ya & Park, Ju H. & Huang, Huan, 2016. "L2–L∞ filtering for stochastic systems driven by Poisson processes and Wiener processes," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 407-416.
    8. Chu, Angus C. & Cozzi, Guido & Furukawa, Yuichi, 2016. "Unions, innovation and cross-country wage inequality," Journal of Economic Dynamics and Control, Elsevier, vol. 64(C), pages 104-118.
    9. Heijs, Joost, 2003. "Freerider behaviour and the public finance of R&D activities in enterprises: the case of the Spanish low interest credits for R&D," Research Policy, Elsevier, vol. 32(3), pages 445-461, March.
    10. Kawalec Paweł, 2020. "The dynamics of theories of economic growth: An impact of Unified Growth Theory," Economics and Business Review, Sciendo, vol. 6(2), pages 19-44, June.
    11. Gilberto Tadeu Lima, 2000. "Market concentration and technological innovation in a dynamic model of growth and distribution," BNL Quarterly Review, Banca Nazionale del Lavoro, vol. 53(215), pages 447-475.
    12. Loebbing, Jonas, 2018. "An Elementary Theory of Endogenous Technical Change and Wage Inequality," VfS Annual Conference 2018 (Freiburg, Breisgau): Digital Economy 181603, Verein für Socialpolitik / German Economic Association.
    13. Grimaud, Andre & Rouge, Luc, 2003. "Non-renewable resources and growth with vertical innovations: optimum, equilibrium and economic policies," Journal of Environmental Economics and Management, Elsevier, vol. 45(2, Supple), pages 433-453, March.
    14. Liliana Meza-González & Jaime Marie Sepulveda, 2019. "The impact of competition with China in the US market on innovation in Mexican manufacturing firms," Latin American Economic Review, Springer;Centro de Investigaciòn y Docencia Económica (CIDE), vol. 28(1), pages 1-21, December.
    15. van de Klundert, T.C.M.J. & Smulders, J.A., 1991. "Reconstructing growth theory : A survey," Other publications TiSEM 19355c51-17eb-4d5d-aa66-b, Tilburg University, School of Economics and Management.
    16. Patrick Legros & Andrew F. Newman & Eugenio Proto, 2014. "Smithian Growth through Creative Organization," The Review of Economics and Statistics, MIT Press, vol. 96(5), pages 796-811, December.
    17. Tung Liu & Kui-Wai Li, 2008. "Revisiting Solow’s Decomposition of Economic and Productivity Growth," Working Papers 200805, Ball State University, Department of Economics, revised Dec 2008.
    18. Bruneel, Johan & Clarysse, Bart & Bobelyn, Annelies & Wright, Mike, 2020. "Liquidity events and VC-backed academic spin-offs: The role of search alliances," Research Policy, Elsevier, vol. 49(10).
    19. Karlsson, Martin & Nilsson, Therese & Pichler, Stefan, 2012. "What Doesn't Kill You Makes You Stronger? The Impact of the 1918 Spanish Flu Epidemic on Economic Performance in Sweden," Working Paper Series 911, Research Institute of Industrial Economics.
    20. Patricia Crifo & Etienne Lehmann, 2001. "Why the Kuznets Curve Will Always Reverse," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00150324, HAL.

    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:apmaco:v:392:y:2021:i:c:s009630032030669x. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.