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Hierarchic Control for the Wave Equation

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Abstract

This paper deals with the hierarchical control of the wave equation. We use Stackelberg–Nash strategies. As usual, we consider one leader and two followers. To each leader we associate a Nash equilibrium corresponding to a bi-objective optimal control problem; then, we look for a leader that solves an exact controllability problem. We consider linear and semilinear equations.

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Acknowledgements

Fágner Dias Araruna has been partially supported by INCTMat, CAPES, CNPq (Brazil), and MathAmSud COSIP. Enrique Fernández-Cara has been partially supported by Grant MTM2016-76990-P (DGI-MICINN, Spain) and CAPES (Brazil). Luciano Cipriano da Silva has been partially supported by CAPES (Brazil).

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Authors and Affiliations

  1. Dpto. de Matemática, Universidade Federal da Paraíba, João Pessoa, PB, 58051-900, Brazil

    Fágner Dias Araruna & Luciano Cipriano da Silva

  2. Dpto. EDAN and IMUS, Universidad de Sevilla, Aptdo. 1160, 41080, Sevilla, Spain

    Enrique Fernández-Cara

Authors
  1. Fágner Dias Araruna
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  2. Enrique Fernández-Cara
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  3. Luciano Cipriano da Silva
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Correspondence to Fágner Dias Araruna.

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Communicated by Enrique Zuazua.

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Araruna, F.D., Fernández-Cara, E. & da Silva, L.C. Hierarchic Control for the Wave Equation. J Optim Theory Appl 178, 264–288 (2018). https://doi.org/10.1007/s10957-018-1277-6

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  • DOI: https://doi.org/10.1007/s10957-018-1277-6

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