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Control of Fluid Flow pp 139–156Cite as

Distributed Control and Observation

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Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 330))

Abstract

Over the recent years, mostly under the impetus of the late JL Lions, important progress have been made for the control of distributed systems. This has contributed to the understanding of the duality which exist between the modal analysis and the need of very localized actuators. This duality leads to the phenomena of overspilling (excitation of higher order modes). On the other hand this type of research is closely related to the analysis of the exterior problem for the acoustic equation which was, under the influence of P. Lax, one of the main stimulus for the development of microlocal analysis. In this contribution only the acoustic equation is studied. However most of the idea carry on to other linear equations and to some non linear equations when considered in a perturbative regime where linearization techniques can be used; this includes perturbations of given solution of the Navier Stokes equation following the work of Imanuvilov and Fursikov (cf [12]) for a recent reference. Same ideas are used also in identification problems for instance in the migration method for oil recovery.

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Author information

Authors and Affiliations

  1. University Denis Diderot and LANN University Pierre et Marie Curie Paris, Paris

    Claude Bardos

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  1. Claude Bardos
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Editor information

Editors and Affiliations

  1. ETH Zürich, CH-8092 Zürich, Switzerland

    Petros Koumoutsakos (Professor of Computational Science) (Professor of Computational Science)

  2. Department of Mechanical Engineering, University of California Santa Barbara, Santa Barbara, CA, 93106, USA

    Igor Mezic

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© 2006 Springer-Verlag Berlin Heidelberg

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Bardos, C. (2006). Distributed Control and Observation. In: Koumoutsakos, P., Mezic, I. (eds) Control of Fluid Flow. Lecture Notes in Control and Information Sciences, vol 330. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-36085-8_6

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  • DOI: https://doi.org/10.1007/978-3-540-36085-8_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25140-8

  • Online ISBN: 978-3-540-36085-8

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