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dc.contributor.authorPrivat, Y.
dc.contributor.authorTrélat, E.
dc.contributor.authorZuazua, E.
dc.date.accessioned2016-06-13T13:33:49Z
dc.date.available2016-06-13T13:33:49Z
dc.date.issued2014-12-31
dc.identifier.isbn978-1-479-93272-6
dc.identifier.issn0743-1619
dc.identifier.urihttp://hdl.handle.net/20.500.11824/229
dc.description.abstractWe 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.
dc.formatapplication/pdf
dc.language.isoengen_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.subjectLinear systems
dc.subjectObservability
dc.subjectOptimization
dc.subjectPartial differential equations
dc.subjectQuantum theory
dc.subjectSpectrum analysis
dc.subjectDistributed parameter systems
dc.subjectEvolution systems
dc.subjectPartial differential equations (PDE)
dc.subjectPartial observation
dc.subjectQuantum ergodicity
dc.subjectSensors and actuators
dc.subjectSensors or actuators
dc.subjectSpace dimensions
dc.subjectActuators
dc.titleOptimal shape and location of sensors or actuators in PDE models
dc.typeinfo:eu-repo/semantics/conferenceObjecten_US
dc.identifier.doi10.1109/ACC.2014.6858664
dc.relation.publisherversionhttp://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=6858664&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D6858664
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/acceptedVersionen_US
dc.journal.titleProceedings of the American Control Conferenceen_US


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