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Regional Robustness Optimal Control Via Strong Stabilization of Semilinear Systems

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Recent Advances in Modeling, Analysis and Systems Control: Theoretical Aspects and Applications

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 243))

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Abstract

The aim of this paper is to treat the problem of regional optimal stabilization of a class of nonlinear systems by using a switching feedback. Firstly, we proof that the switching control strongly stabilize the system on subregion includes in the whole domain. Secondly, under a perturbation of the control operator we show the robustness of our result. In the last part the stabilizing feedback is characterized by the minimization of a regional cost even under a small perturbation. We conclude by giving different applications to hyperbolic and parabolic equations.

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Acknowledgements

This work has been carried out with a grant from Hassan II Academy of Sciences and Technology project N\(^\circ \) 630/2016.

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Authors and Affiliations

  1. TSI Team, MACS Laboratory, Department of Mathematics and Computer Science, Faculty of Sciences, Moulay Ismail University, Meknes, Morocco

    Abdessamad El Alami & Ali Boutoulout

Authors
  1. Abdessamad El Alami
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  2. Ali Boutoulout
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Corresponding author

Correspondence to Abdessamad El Alami .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Moulay Ismail University, Zitoune Meknès, Morocco

    El Hassan Zerrik

  2. Department of Mathematics, Sultan Moulay Slimane University, Beni Mellal, Morocco

    Said Melliani

  3. Division of Graduate Studies and Research, Tijuana Institute of Technology, Tijuana, Mexico

    Oscar Castillo

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El Alami, A., Boutoulout, A. (2020). Regional Robustness Optimal Control Via Strong Stabilization of Semilinear Systems. In: Zerrik, E., Melliani, S., Castillo, O. (eds) Recent Advances in Modeling, Analysis and Systems Control: Theoretical Aspects and Applications. Studies in Systems, Decision and Control, vol 243. Springer, Cham. https://doi.org/10.1007/978-3-030-26149-8_6

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