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

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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
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    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. 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.
    3. 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.
    4. 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.
    5. 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.
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    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).

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