Self-adjoint differential-algebraic equations
dc.contributor.author | Kunkel, Peter | |
dc.contributor.author | Mehrmann, Volker | |
dc.contributor.author | Scholz, Lena | |
dc.date.accessioned | 2021-12-17T10:09:41Z | |
dc.date.available | 2021-12-17T10:09:41Z | |
dc.date.issued | 2011-07-07 | |
dc.description.abstract | Motivated from linear-quadratic optimal control problems for differential-algebraic equations (DAEs), we study the functional analytic properties of the operator associated with the necessary optimality boundary value problem and show that it is associated with a self-conjugate operator and a self-adjoint pair of matrix functions. We then study general self-adjoint pairs of matrix valued functions and derive condensed forms under orthogonal congruence transformations that preserve the self-adjointness. We analyze the relationship between self-adjoint DAEs and Hamiltonian systems with symplectic flows. We also show how to extract self-adjoint and Hamiltonian reduced systems from derivative arrays. | en |
dc.identifier.issn | 2197-8085 | |
dc.identifier.uri | https://depositonce.tu-berlin.de/handle/11303/15718 | |
dc.identifier.uri | http://dx.doi.org/10.14279/depositonce-14491 | |
dc.language.iso | en | en |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
dc.subject.ddc | 510 Mathematik | en |
dc.subject.other | differential-algebraic equation | en |
dc.subject.other | self-conjugate operator | en |
dc.subject.other | self-adjoint pair | en |
dc.subject.other | optimal control | en |
dc.subject.other | necessary optimality condition | en |
dc.subject.other | strangeness index | en |
dc.subject.other | condensed form | en |
dc.subject.other | congruence transformation | en |
dc.subject.other | Hamiltonian system | en |
dc.subject.other | symplectic flow | en |
dc.title | Self-adjoint differential-algebraic equations | en |
dc.type | Research Paper | en |
dc.type.version | submittedVersion | en |
tub.accessrights.dnb | free | en |
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 | 2011, 13 | en |
tub.series.name | Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin | en |
tub.subject.msc2000 | 93C10 Nonlinear systems | en |
tub.subject.msc2000 | 93C15 Systems governed by ordinary differential equations | en |
tub.subject.msc2000 | 93B52 Feedback control | en |
tub.subject.msc2000 | 65L80 Methods for differential-algebraic equations | en |
tub.subject.msc2000 | 49K15 Problems involving ordinary differential equations | en |
tub.subject.msc2000 | 34H05 Control problems | en |
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