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Optimal feedback control for a class of fractional evolution equations with history-dependent operators

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Abstract

In this paper, we will study optimal feedback control problems derived by a class of Riemann-Liouville fractional evolution equations with history-dependent operators in separable reflexive Banach spaces. We firstly introduce suitable hypotheses to prove the existence and uniqueness of mild solutions for this kind of Riemann-Liouville fractional evolution equations with history-dependent operators. Then, by introducing a feedback iterative technique and applying Filippov theorem, we show the existence of feasible pairs and optimal control pairs of the optimal feedback control systems with history-dependent operators. Finally, we give some applications to illustrate our main results.

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Acknowledgements

Project supported by NNSF of China Grant Nos. 11961074, 12071413; NSF of Guangxi Grant No. 2018GXNSFDA281028.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Yulin Normal University, Yulin, 537000, Guangxi, People’s Republic of China

    Yongjian Liu

  2. Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi Minzu University, Nanning, 530006, Guangxi, People’s Republic of China

    Zhenhai Liu & Sisi Peng

  3. Center for Fundamental Science, and Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung, 80708, Taiwan

    Ching-Feng Wen

  4. Department of Medical Research, Kaohsiung Medical University Hospital, Kaohsiung, 80708, Taiwan

    Ching-Feng Wen

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  1. Yongjian Liu
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  2. Zhenhai Liu
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  3. Sisi Peng
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  4. Ching-Feng Wen
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Correspondence to Ching-Feng Wen.

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Liu, Y., Liu, Z., Peng, S. et al. Optimal feedback control for a class of fractional evolution equations with history-dependent operators. Fract Calc Appl Anal 25, 1108–1130 (2022). https://doi.org/10.1007/s13540-022-00054-y

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  • DOI: https://doi.org/10.1007/s13540-022-00054-y

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