Self-adjoint differential-algebraic equations

dc.contributor.authorKunkel, Peter
dc.contributor.authorMehrmann, Volker
dc.contributor.authorScholz, Lena
dc.date.accessioned2021-12-17T10:09:41Z
dc.date.available2021-12-17T10:09:41Z
dc.date.issued2011-07-07
dc.description.abstractMotivated 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.issn2197-8085
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/15718
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-14491
dc.language.isoenen
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.ddc510 Mathematiken
dc.subject.otherdifferential-algebraic equationen
dc.subject.otherself-conjugate operatoren
dc.subject.otherself-adjoint pairen
dc.subject.otheroptimal controlen
dc.subject.othernecessary optimality conditionen
dc.subject.otherstrangeness indexen
dc.subject.othercondensed formen
dc.subject.othercongruence transformationen
dc.subject.otherHamiltonian systemen
dc.subject.othersymplectic flowen
dc.titleSelf-adjoint differential-algebraic equationsen
dc.typeResearch Paperen
dc.type.versionsubmittedVersionen
tub.accessrights.dnbfreeen
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.issuenumber2011, 13en
tub.series.namePreprint-Reihe des Instituts für Mathematik, Technische Universität Berlinen
tub.subject.msc200093C10 Nonlinear systemsen
tub.subject.msc200093C15 Systems governed by ordinary differential equationsen
tub.subject.msc200093B52 Feedback controlen
tub.subject.msc200065L80 Methods for differential-algebraic equationsen
tub.subject.msc200049K15 Problems involving ordinary differential equationsen
tub.subject.msc200034H05 Control problemsen

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