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Internal Layer Solution of Singularly Perturbed Optimal Control Problem with Integral Boundary Condition

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Abstract

In this paper, we investigate a class of singularly perturbed optimal control problem with integral boundary condition. By means of \(k+\sigma \) exchange lemma, the existence of internal layer solution for the optimal control problem is proved. Meanwhile, the uniformly valid asymptotic solution is constructed by the boundary function method. Finally, an example is given for illustrating the main result.

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Acknowledgements

This project is supported by the Natural Science Foundation of Hebei Province (A2015407063), National Natural Science Foundation of China (Nos. 11471118, 11401385 and 11371140) and Doctoral Foundation of Hebei Normal University of Science and Technology (2013YB008). The authors wish to thank the editors and reviewers for their conscientious reading of this paper and their comments for improvement which were extremely useful and helpful in modifying the paper.

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Authors and Affiliations

  1. School of Mathematics and Information Technology, Hebei Normal University of Science and Technology, Qinhuangdao, 066004, China

    Limeng Wu

  2. Department of Mathematics, East China Normal University, Shanghai, 200241, China

    Mingkang Ni

  3. School of Economics and Management, Shanghai Institute of Technology, Shanghai, 201418, China

    Haibo Lu

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  1. Limeng Wu
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  2. Mingkang Ni
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  3. Haibo Lu
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Correspondence to Mingkang Ni.

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Wu, L., Ni, M. & Lu, H. Internal Layer Solution of Singularly Perturbed Optimal Control Problem with Integral Boundary Condition. Qual. Theory Dyn. Syst. 17, 49–66 (2018). https://doi.org/10.1007/s12346-017-0261-0

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  • DOI: https://doi.org/10.1007/s12346-017-0261-0

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