IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v182y2019i2d10.1007_s10957-018-1313-6.html
   My bibliography  Save this article

Time Optimal Control of a System Governed by Non-instantaneous Impulsive Differential Equations

Author

Listed:
  • JinRong Wang

    (Guizhou University)

  • Michal Fečkan

    (Comenius University in Bratislava
    Mathematical Institute, Slovak Academy of Sciences)

  • Amar Debbouche

    (Guelma University)

Abstract

We investigate time optimal control of a system governed by a class of non-instantaneous impulsive differential equations in Banach spaces. We use an appropriate linear transformation technique to transfer the original impulsive system into an approximate one, and then we prove the existence and uniqueness of their mild solutions. Moreover, we show the existence of optimal controls for Meyer problems of the approximate. Further, in order to solve the time optimal control problem for the original system, we construct a sequence of Meyer approximations for which the desired optimal control and optimal time are well derived.

Suggested Citation

  • JinRong Wang & Michal Fečkan & Amar Debbouche, 2019. "Time Optimal Control of a System Governed by Non-instantaneous Impulsive Differential Equations," Journal of Optimization Theory and Applications, Springer, vol. 182(2), pages 573-587, August.
  • Handle: RePEc:spr:joptap:v:182:y:2019:i:2:d:10.1007_s10957-018-1313-6
    DOI: 10.1007/s10957-018-1313-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-018-1313-6
    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/s10957-018-1313-6?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. Agarwal, Ravi & O'Regan, D. & Hristova, S., 2017. "Monotone iterative technique for the initial value problem for differential equations with non-instantaneous impulses," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 45-56.
    2. Amar Debbouche & Juan J. Nieto & Delfim F. M. Torres, 2017. "Optimal Solutions to Relaxation in Multiple Control Problems of Sobolev Type with Nonlocal Nonlinear Fractional Differential Equations," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 7-31, July.
    3. Abbas, Saïd & Benchohra, Mouffak, 2015. "Uniqueness and Ulam stabilities results for partial fractional differential equations with not instantaneous impulses," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 190-198.
    4. Shengda Liu & JinRong Wang, 2017. "Optimal Controls of Systems Governed by Semilinear Fractional Differential Equations with Not Instantaneous Impulses," Journal of Optimization Theory and Applications, Springer, vol. 174(2), pages 455-473, August.
    5. JinRong Wang & Michal Fec̆kan & Yong Zhou, 2013. "Relaxed Controls for Nonlinear Fractional Impulsive Evolution Equations," Journal of Optimization Theory and Applications, Springer, vol. 156(1), pages 13-32, January.
    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. Cheng, Yingying & Huo, Liang'an & Zhao, Laijun, 2022. "Stability analysis and optimal control of rumor spreading model under media coverage considering time delay and pulse vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    2. Kumar, Vipin & Malik, Muslim & Debbouche, Amar, 2021. "Stability and controllability analysis of fractional damped differential system with non-instantaneous impulses," Applied Mathematics and Computation, Elsevier, vol. 391(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. Amit K Verma & Biswajit Pandit & Ravi P. Agarwal, 2021. "Analysis and Computation of Solutions for a Class of Nonlinear SBVPs Arising in Epitaxial Growth," Mathematics, MDPI, vol. 9(7), pages 1-25, April.
    2. Mallika Arjunan, M. & Abdeljawad, Thabet & Kavitha, V. & Yousef, Ali, 2021. "On a new class of Atangana-Baleanu fractional Volterra-Fredholm integro-differential inclusions with non-instantaneous impulses," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    3. shu, Xiao-Bao & Shi, Yajing, 2016. "A study on the mild solution of impulsive fractional evolution equations," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 465-476.
    4. Yong-Kui Chang & Yatian Pei & Rodrigo Ponce, 2019. "Existence and Optimal Controls for Fractional Stochastic Evolution Equations of Sobolev Type Via Fractional Resolvent Operators," Journal of Optimization Theory and Applications, Springer, vol. 182(2), pages 558-572, August.
    5. Rosa, Silvério & Torres, Delfim F.M., 2018. "Optimal control of a fractional order epidemic model with application to human respiratory syncytial virus infection," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 142-149.
    6. Yang, Dan & Wang, JinRong & O’Regan, D., 2018. "A class of nonlinear non-instantaneous impulsive differential equations involving parameters and fractional order," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 654-671.
    7. Haide Gou & Tianxiang Wang, 2023. "The method of lower and upper solution for Hilfer evolution equations with non-instantaneous impulses," Indian Journal of Pure and Applied Mathematics, Springer, vol. 54(2), pages 499-523, June.
    8. Yan, Zuomao & Lu, Fangxia, 2017. "Approximate controllability of a multi-valued fractional impulsive stochastic partial integro-differential equation with infinite delay," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 425-447.
    9. Dhayal, Rajesh & Malik, Muslim, 2021. "Approximate controllability of fractional stochastic differential equations driven by Rosenblatt process with non-instantaneous impulses," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    10. Surang Sitho & Chayapat Sudprasert & Sotiris K. Ntouyas & Jessada Tariboon, 2020. "Noninstantaneous Impulsive Fractional Quantum Hahn Integro-Difference Boundary Value Problems," Mathematics, MDPI, vol. 8(5), pages 1-15, April.
    11. Surendra Kumar, 2017. "Mild Solution and Fractional Optimal Control of Semilinear System with Fixed Delay," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 108-121, July.
    12. Yao-Qun Wu & Jia Wei He, 2022. "Existence and Optimal Controls for Hilfer Fractional Sobolev-Type Stochastic Evolution Equations," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 79-101, October.
    13. Liu, Kui & Wang, JinRong & Zhou, Yong & O’Regan, Donal, 2020. "Hyers–Ulam stability and existence of solutions for fractional differential equations with Mittag–Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    14. Shengda Liu & JinRong Wang, 2017. "Optimal Controls of Systems Governed by Semilinear Fractional Differential Equations with Not Instantaneous Impulses," Journal of Optimization Theory and Applications, Springer, vol. 174(2), pages 455-473, August.
    15. Rafał Kamocki & Marek Majewski, 2017. "On the Existence and Continuous Dependence on Parameter of Solutions to Some Fractional Dirichlet Problem with Application to Lagrange Optimal Control Problem," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 32-46, July.
    16. Li, Mengmeng & Wang, JinRong, 2018. "Exploring delayed Mittag-Leffler type matrix functions to study finite time stability of fractional delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 254-265.
    17. Chen Bin & Xiao Yu Liang & Emil Minchev & Sergey A. Timoshin, 2023. "Optimization of a Prey–Predator Model with Hysteresis and Convection," Journal of Optimization Theory and Applications, Springer, vol. 198(1), pages 347-371, July.
    18. Yu Chen & JinRong Wang, 2019. "Continuous Dependence of Solutions of Integer and Fractional Order Non-Instantaneous Impulsive Equations with Random Impulsive and Junction Points," Mathematics, MDPI, vol. 7(4), pages 1-13, April.

    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:182:y:2019:i:2:d:10.1007_s10957-018-1313-6. 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.