IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i19p3478-d923369.html
   My bibliography  Save this article

Collision Avoidance Problem of Ellipsoid Motion

Author

Listed:
  • Shujun Guo

    (School of Business, Qingdao University, Qingdao 266071, China)

  • Lujing Jing

    (School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China)

  • Zhaopeng Dai

    (School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China)

  • Yang Yu

    (School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China)

  • Zhiqing Dang

    (School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China)

  • Zhihang You

    (School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China)

  • Ang Su

    (School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China)

  • Hongwei Gao

    (School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China
    College of Science, Jiamusi University, Jiamusi 154007, China)

  • Jinqiu Guan

    (College of Science, Jiamusi University, Jiamusi 154007, China)

  • Yujun Song

    (College of Science, Jiamusi University, Jiamusi 154007, China)

Abstract

This paper studies the problem of target control and how a virtual ellipsoid can avoid the static obstacle. During the motion to the target set, the virtual ellipsoid can achieve a motion under collision avoidance by keeping the distance between the ellipsoid and obstacle. We present solutions to this problem in the class of closed-loop (feedback) controls based on Hamilton–Jacobi–Bellman (HJB) equation. Simulation results verify the validity and effectiveness of our algorithm.

Suggested Citation

  • Shujun Guo & Lujing Jing & Zhaopeng Dai & Yang Yu & Zhiqing Dang & Zhihang You & Ang Su & Hongwei Gao & Jinqiu Guan & Yujun Song, 2022. "Collision Avoidance Problem of Ellipsoid Motion," Mathematics, MDPI, vol. 10(19), pages 1-12, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3478-:d:923369
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/19/3478/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/19/3478/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. A. B. Kurzhanski & I. M. Mitchell & P. Varaiya, 2006. "Optimization Techniques for State-Constrained Control and Obstacle Problems," Journal of Optimization Theory and Applications, Springer, vol. 128(3), pages 499-521, March.
    2. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329.
    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. Masahiko Hattori & Yasuhito Tanaka, 2019. "General analysis of dynamic oligopoly with sticky price," Economics Bulletin, AccessEcon, vol. 39(4), pages 2990-2998.
    2. Luca Lambertini & Arsen Palestini & Alessandro Tampieri, 2016. "CSR in an Asymmetric Duopoly with Environmental Externality," Southern Economic Journal, John Wiley & Sons, vol. 83(1), pages 236-252, July.
    3. Açıkgöz, Ömer T. & Benchekroun, Hassan, 2017. "Anticipated international environmental agreements," European Economic Review, Elsevier, vol. 92(C), pages 306-336.
    4. Xiaochi Wu, 2022. "Existence of value for a differential game with asymmetric information and signal revealing," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(1), pages 213-247, March.
    5. Régis Chenavaz & Corina Paraschiv & Gabriel Turinici, 2017. "Dynamic Pricing of New Products in Competitive Markets: A Mean-Field Game Approach," Working Papers hal-01592958, HAL.
    6. Reinhard Neck & Dmitri Blueschke, 2014. "“Haircuts” for the EMU periphery: virtue or vice?," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 41(2), pages 153-175, May.
    7. Benchekroun, Hassan & Ray Chaudhuri, Amrita & Tasneem, Dina, 2020. "On the impact of trade in a common property renewable resource oligopoly," Journal of Environmental Economics and Management, Elsevier, vol. 101(C).
    8. A. J. Novak & G. Feichtinger & G. Leitmann, 2010. "A Differential Game Related to Terrorism: Nash and Stackelberg Strategies," Journal of Optimization Theory and Applications, Springer, vol. 144(3), pages 533-555, March.
    9. Gerhard Sorger, 2005. "A dynamic common property resource problem with amenity value and extraction costs," International Journal of Economic Theory, The International Society for Economic Theory, vol. 1(1), pages 3-19, March.
    10. Mukherjee, Arka & Carvalho, Margarida, 2021. "Dynamic decision making in a mixed market under cooperation: Towards sustainability," International Journal of Production Economics, Elsevier, vol. 241(C).
    11. Smala Fanokoa, Pascaux & Telahigue, Issam & Zaccour, Georges, 2011. "Buying cooperation in an asymmetric environmental differential game," Journal of Economic Dynamics and Control, Elsevier, vol. 35(6), pages 935-946, June.
    12. Hilli, Amal & Laussel, Didier & Van Long, Ngo, 2013. "Large shareholders, monitoring, and ownership dynamics: Toward pure managerial firms?," Journal of Economic Dynamics and Control, Elsevier, vol. 37(3), pages 666-679.
    13. Denis Claude & Charles Figuières & Mabel Tidball, 2008. "Short-run stick and long-run carrot policy: the role of initial conditions," Working Papers 08-04, LAMETA, Universtiy of Montpellier, revised Feb 2008.
    14. Anna Castañer & Jesús Marín-Solano & Carmen Ribas, 2021. "A time consistent dynamic bargaining procedure in differential games with hterogeneous discounting," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(3), pages 555-584, June.
    15. Günther Rehme, 2023. "Capital depreciation allowances, redistributive taxation, and economic growth," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 25(1), pages 168-195, February.
    16. Stergios Athanassoglou & Glenn Sheriff & Tobias Siegfried & Woonghee Huh, 2012. "Optimal Mechanisms for Heterogeneous Multi-Cell Aquifers," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 52(2), pages 265-291, June.
    17. Wirl, Franz, 2014. "Taxes versus permits as incentive for the intertemporal supply of a clean technology by a monopoly," Resource and Energy Economics, Elsevier, vol. 36(1), pages 248-269.
    18. Francesca Calà Campana & Gabriele Ciaramella & Alfio Borzì, 2021. "Nash Equilibria and Bargaining Solutions of Differential Bilinear Games," Dynamic Games and Applications, Springer, vol. 11(1), pages 1-28, March.
    19. S. Luckraz, 2008. "Process Spillovers and Growth," Journal of Optimization Theory and Applications, Springer, vol. 139(2), pages 315-335, November.
    20. Mukherjee, Arka & Chauhan, Satyaveer S., 2021. "The impact of product recall on advertising decisions and firm profit while envisioning crisis or being hazard myopic," European Journal of Operational Research, Elsevier, vol. 288(3), pages 953-970.

    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:gam:jmathe:v:10:y:2022:i:19:p:3478-:d:923369. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.