Optimal shape and location of sensors or actuators in PDE models

Privat Y, Trelat E, Zuazua E (2014)

Publication Type: Conference contribution

Publication year: 2014

Journal

Proceedings of the American Control Conference

Publisher: Institute of Electrical and Electronics Engineers Inc.

Pages Range: 4063-4068

Conference Proceedings Title: Proceedings of the American Control Conference

Event location: USA

ISBN: 9781479932726

DOI: 10.1109/ACC.2014.6858664

Abstract

We investigate the problem of optimizing the shape and location of sensors and actuators for evolution systems driven by distributed parameter systems or partial differential equations (PDE). We consider wave, Schrödinger and heat equations on an arbitrary domain Ω, in any space dimension, and with suitable boundary conditions (if there is a boundary) which can be of Dirichlet, Neumann, mixed or Robin type. This kind of problem is frequently encountered in applications where one aims, for instance, at maximizing the quality of reconstruction of the solution, using only a partial observation. From the mathematical point of view, using probabilistic considerations we model this problem as that of maximizing the so-called randomized observability constant, over all possible subdomains of Ω having a prescribed measure. The spectral analysis of this problem reveals intimate connections with the theory of quantum chaos. More precisely, we provide a solution to this problem when the domain Ω satisfies suitable quantum ergodicity assumptions. © 2014 American Automatic Control Council.

Authors with CRIS profile

Enrique Zuazua Iriondo

Involved external institutions

University of Paris 6 - Pierre et Marie Curie / Université Paris VI Pierre et Marie Curie (UPMC) FR France (FR) Basque Center of Applied Mathematics (BCAM) ES Spain (ES)

How to cite

APA:

Privat, Y., Trelat, E., & Zuazua, E. (2014). Optimal shape and location of sensors or actuators in PDE models. In Proceedings of the American Control Conference (pp. 4063-4068). USA: Institute of Electrical and Electronics Engineers Inc..

MLA:

Privat, Yannick, Emmanuel Trelat, and Enrique Zuazua. "Optimal shape and location of sensors or actuators in PDE models." Proceedings of the 2014 American Control Conference, ACC 2014, USA Institute of Electrical and Electronics Engineers Inc., 2014. 4063-4068.

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