Systematic discretization of input-output maps of linear infinite dimensional systems (revised)
dc.contributor.author | Schmidt, Michael | |
dc.date.accessioned | 2022-05-11T12:11:39Z | |
dc.date.available | 2022-05-11T12:11:39Z | |
dc.date.issued | 2008-08-21 | |
dc.description | This 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.abstract | Many 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.issn | 2197-8085 | |
dc.identifier.uri | https://depositonce.tu-berlin.de/handle/11303/16893 | |
dc.identifier.uri | http://dx.doi.org/10.14279/depositonce-15671 | |
dc.language.iso | en | |
dc.relation.isversionof | 10.14279/depositonce-15654 | |
dc.relation.references | 10.14279/depositonce-1600 | |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | |
dc.subject.ddc | 510 Mathematik | en |
dc.subject.other | input-output map | en |
dc.subject.other | discretization | en |
dc.subject.other | infinite-dimensional control system | en |
dc.subject.other | time-discrete MIMO system | en |
dc.subject.other | model reduction | en |
dc.subject.other | optimization | en |
dc.subject.other | feedback control | en |
dc.title | Systematic discretization of input-output maps of linear infinite dimensional systems (revised) | en |
dc.type | Research Paper | en |
dc.type.version | submittedVersion | en |
tub.accessrights.dnb | free | |
tub.affiliation | Fak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik | de |
tub.affiliation.faculty | Fak. 2 Mathematik und Naturwissenschaften | de |
tub.affiliation.institute | Inst. Mathematik | de |
tub.publisher.universityorinstitution | Technische Universität Berlin | en |
tub.series.issuenumber | 2008, 29 | en |
tub.series.name | Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin | en |
tub.subject.msc2000 | 93C20 Systems governed by partial differential equations | en |
tub.subject.msc2000 | 35B37 PDE in connection with control problems | en |
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