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Sensitivity analysis for optimal control problems described by nonlinear fractional evolution inclusions

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Abstract

In this paper, a sensitivity analysis of optimal control problem for a class of systems described by nonlinear fractional evolution inclusions (NFEIs, for short) on Banach spaces is investigated. Firstly, the nonemptiness as well as the compactness of the mild solutions set S(ζ) (ζ being the initial condition) for the NFEIs are obtained, and we also present an extension Filippov’s theorem and whose proof differs from previous work only in some technical details. Finally, the optimal control problems described by NFEIs depending on the initial condition ζ and the parameter η are considered and the sensitivity properties of the optimal control problem are also established.

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Authors and Affiliations

  1. School of Science, Nanjing University of Sciences and Technology Nanjing, Jiangsu Province, P.R. China

    Xiuwen Li

  2. Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing Yulin Normal University, Yulin, 537000, P.R. China

    Yunxiang Li

  3. College of Sciences, Guangxi University for Nationalities Nanning, Guangxi Province, P.R. China

    Zhenhai Liu

  4. Hunan Province Key Laboratory of Mathematical Modelling and Analysis in Engineering, Department of Mathematics and Statistics Changsha University of Science and Technology, Changsha, 410114, P.R. China

    Jing Li

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  1. Xiuwen Li
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Correspondence to Xiuwen Li.

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Li, X., Li, Y., Liu, Z. et al. Sensitivity analysis for optimal control problems described by nonlinear fractional evolution inclusions. FCAA 21, 1439–1470 (2018). https://doi.org/10.1515/fca-2018-0076

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