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Some Remarks on the Hierarchic Control for Coupled Parabolic PDEs

  • Víctor Hernández-Santamaría
  • Luz de TeresaEmail author
Chapter
Part of the SEMA SIMAI Springer Series book series (SEMA SIMAI, volume 17)

Abstract

In this paper, we study Stackelberg-Nash strategies to control a system of two coupled parabolic equations. We assume that we act in the system by means of a hierarchy of controls. First, a leader (vectorial) control achieve their objectives, and then other controls, named followers, react optimally to the leader action. We prove an observability inequality for an extended system, which yields the Stackelberg-Nash optimization. Then, we remove the action of one of the components of the leader control. In this way, we control a system of various equations by acting only on the first component.

Keywords

Controllabilty Stackelberg-Nash strategies Carleman inequalities parabolic systems 

Notes

Acknowledgements

This work was partially supported by CONACyT and UNAM-DGAPA-PAPIIT IN102116.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Víctor Hernández-Santamaría
    • 1
  • Luz de Teresa
    • 2
    Email author
  1. 1.Depto. de Control AutomáticoCINVESTAV-IPNCiudad de MéxicoMexico
  2. 2.Instituto de MatemáticasUniversidad Nacional Autónoma de MéxicoMexico CityMexico

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