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Mild Solution and Fractional Optimal Control of Semilinear System with Fixed Delay

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  • Surendra Kumar

    (University of Delhi)

Abstract

This paper considers fractional optimal control of a semilinear system with fixed delay in a reflexive Banach space. The existence and uniqueness of mild solution are obtained using the Weissinger’s fixed point theorem. The existence of optimal control for the system governed by fractional-order semilinear equation with fixed delay in state is presented. To show the effectiveness of the developed theory, an example is given.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:174:y:2017:i:1:d:10.1007_s10957-015-0828-3
    DOI: 10.1007/s10957-015-0828-3
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Tian Liang Guo, 2013. "The Necessary Conditions of Fractional Optimal Control in the Sense of Caputo," Journal of Optimization Theory and Applications, Springer, vol. 156(1), pages 115-126, January.
    4. Jin-Mun Jeong & Sang-Jin Son, 2015. "Time Optimal Control of Semilinear Control Systems Involving Time Delays," Journal of Optimization Theory and Applications, Springer, vol. 165(3), pages 793-811, June.
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    Cited by:

    1. Yang, He & Zhao, Yanxia, 2021. "Existence and optimal controls of non-autonomous impulsive integro-differential evolution equation with nonlocal conditions," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).

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