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Properties of the Set of Admissible “State Control” Pair for a Class of Fractional Semilinear Evolution Control Systems

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Abstract

In this paper, we discuss a class of Caputo fractional evolution equations on Banach space with feedback control constraint whose value is non-convex closed in the control space. First, we prove the existence of solutions for the system with feedback control whose values are the extreme points of the convexified constraint that belongs to the original one. Secondly, we study the topological properties of the sets of admissible “state-control” pair for the original system with various feedback control constraints and the relations between them. Moreover, we obtain necessary and sufficient conditions for the solution set of original systems to be closed. In the end, an example is given to illustrate the applications of our main results.

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Authors and Affiliations

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

    Maojun Bin & Yunxiang Li

  2. Department of Applied Mathematics, Nanjing Audit University, Nanjing, Jiangsu, 211815, China

    Haiyun Deng

  3. School of Mathematics, Computation Sciences, Hunan City University, Yiyang, 413000, China

    Yunxiang Li

  4. College of Sciences, Beibu Gulf University, Qinzhou, 535000, Guangxi, China

    Zhao Jing

Authors
  1. Maojun Bin
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  2. Haiyun Deng
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  3. Yunxiang Li
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  4. Zhao Jing
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Correspondence to Maojun Bin.

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Bin, M., Deng, H., Li, Y. et al. Properties of the Set of Admissible “State Control” Pair for a Class of Fractional Semilinear Evolution Control Systems. Fract Calc Appl Anal 24, 1275–1298 (2021). https://doi.org/10.1515/fca-2021-0055

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  • DOI: https://doi.org/10.1515/fca-2021-0055

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