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Approximation techniques of optimal control problems for fractional dynamic systems in separable Hilbert spaces

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  • Peng, Li
  • Zhou, Yong
  • Debbouche, Amar

Abstract

We investigate an optimal control problem involving a class of fractional evolution equations in separable Hilbert spaces. The strategy of this paper is establishing low dimensional approximations for this type of equations by using approximation methods. We derive three kinds of convergence results of mild solutions under appropriate assumptions. Then, the convergence result holds for cost functional as well. Further, error estimates of cost functional and optimal controls are obtained. Finally, the proposed concept is supported by an illustrated example.

Suggested Citation

  • Peng, Li & Zhou, Yong & Debbouche, Amar, 2019. "Approximation techniques of optimal control problems for fractional dynamic systems in separable Hilbert spaces," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 234-241.
    • Handle: RePEc:eee:chsofr:v:118:y:2019:i:c:p:234-241
    DOI: 10.1016/j.chaos.2018.11.025
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    References listed on IDEAS

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    1. Atangana, Abdon & Koca, Ilknur, 2016. "Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 447-454.
    2. Atangana, Abdon, 2018. "Non validity of index law in fractional calculus: A fractional differential operator with Markovian and non-Markovian properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 688-706.
    3. JinRong Wang & Yong Zhou & Milan Medveď, 2012. "On the Solvability and Optimal Controls of Fractional Integrodifferential Evolution Systems with Infinite Delay," Journal of Optimization Theory and Applications, Springer, vol. 152(1), pages 31-50, January.
    4. Debbouche, Amar & Antonov, Valery, 2017. "Approximate controllability of semilinear Hilfer fractional differential inclusions with impulsive control inclusion conditions in Banach spaces," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 140-148.
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    Cited by:

    1. 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.
    2. ZOUARI, Farouk & IBEAS, Asier & BOULKROUNE, Abdesselem & CAO, Jinde & AREFI, Mohammad Mehdi, 2021. "Neural network controller design for fractional-order systems with input nonlinearities and asymmetric time-varying Pseudo-state constraints," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).

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