Systematic discretization of input-output maps of linear infinite dimensional systems (revised)

dc.contributor.authorSchmidt, Michael
dc.date.accessioned2022-05-11T12:11:39Z
dc.date.available2022-05-11T12:11:39Z
dc.date.issued2008-08-21
dc.descriptionThis preprint is a completely revised version of Preprint 2006-06. For more details see the dissertation thesis of the author published in 2007.en
dc.description.abstractMany model reduction techniques take a semi-discretization of a PDE model as starting point and aim then at an accurate approximation of its input/output map. In this contribution, we discuss the direct discretization of the i/o map of the infinite-dimensional system for a general class of linear time-invariant systems with distributed inputs and outputs. First, the input and output signals are discretized in space and time, resulting in the matrix representation of an approximated i/o-map. In a generalized sense, the matrix contains the Markov parameters of a corresponding time-discrete multi-input-multi-output system. Second, the system dynamics is approximated in form of the underlying evolution operator, in order to calculate the matrix representation numerically. The discretization framework, corresponding error estimates, a SVD-based system reduction method and a numerical application in an optimization problem are presented, and illustrated for a heat control system.en
dc.identifier.issn2197-8085
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/16893
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-15671
dc.language.isoen
dc.relation.isversionof10.14279/depositonce-15654
dc.relation.references10.14279/depositonce-1600
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subject.ddc510 Mathematiken
dc.subject.otherinput-output mapen
dc.subject.otherdiscretizationen
dc.subject.otherinfinite-dimensional control systemen
dc.subject.othertime-discrete MIMO systemen
dc.subject.othermodel reductionen
dc.subject.otheroptimizationen
dc.subject.otherfeedback controlen
dc.titleSystematic discretization of input-output maps of linear infinite dimensional systems (revised)en
dc.typeResearch Paperen
dc.type.versionsubmittedVersionen
tub.accessrights.dnbfree
tub.affiliationFak. 2 Mathematik und Naturwissenschaften::Inst. Mathematikde
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.instituteInst. Mathematikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen
tub.series.issuenumber2008, 29en
tub.series.namePreprint-Reihe des Instituts für Mathematik, Technische Universität Berlinen
tub.subject.msc200093C20 Systems governed by partial differential equationsen
tub.subject.msc200035B37 PDE in connection with control problemsen

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