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A numerical evaluation of solvers for the periodic Riccati differential equation

Gusev, Sergei und Johansson, Stefan und Kagström, Bo und Shiriaev, Anton und Varga, Andreas (2010) A numerical evaluation of solvers for the periodic Riccati differential equation. BIT Numerical Mathematics. Springer. DOI: 10.1007/s10543-010-0257-5.

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Kurzfassung

Efficient and accurate structure exploiting numerical methods for solving the periodic Riccati differential equation (PRDE) are addressed. Such methods are essential, for example, to design periodic feedback controllers for periodic control systems. Three recently proposed methods for solving the PRDE are presented and evaluated on challenging periodic linear artificial systems with known solutions and applied to the stabilization of periodic motions of mechanical systems. The first two methods are of the type multiple shooting and rely on computing the stable invariant subspace on associated Hamiltonian system. The stable subspace is determined using either algorithms for computing an ordered periodic real Schur form of a cyclic matrix sequence, or a recently proposed method which implicitly constructs a stable deflating subspace from an associated lifted pencil. The third method reformulates the PRDE as a convex optimization problem where the stabilizing solution is approximated by its truncated Fourier series. As known, this reformulations leads to a semi-definite programming problem with linear matrix inequality constraints admitting an effective nuermical realization. The numerical evaluation of the PRDE methods, with focus on the number of states (n) and the length of the period (T) of the periodic systems considered, includes both quantitative and qualitative results.

Dokumentart:Zeitschriftenbeitrag
Titel:A numerical evaluation of solvers for the periodic Riccati differential equation
Autoren:
AutorenInstitution oder E-Mail-Adresse der Autoren
Gusev, SergeiSt. Petersburg State University
Johansson, StefanUmea University
Kagström, BoUmea University
Shiriaev, AntonNorwegian University of Science and Technology
Varga, AndreasAndreas.Varga@dlr.de
Datum:Februar 2010
Erschienen in:BIT Numerical Mathematics
Referierte Publikation:Ja
In Open Access:Nein
In SCOPUS:Ja
In ISI Web of Science:Ja
DOI :10.1007/s10543-010-0257-5
Verlag:Springer
Status:veröffentlicht
Stichwörter:Periodic systems, Periodic Riccati differential equations, Orbital stabilization, Periodic real Schur form, Periodic eigenvalue reordering, Hamiltonian systems, Linear matrix inequalities, Numerical methods
HGF - Forschungsbereich:Luftfahrt, Raumfahrt und Verkehr
HGF - Programm:Luftfahrt
HGF - Programmthema:Starrflügler
DLR - Schwerpunkt:Luftfahrt
DLR - Forschungsgebiet:L AR - Starrflüglerforschung
DLR - Teilgebiet (Projekt, Vorhaben):L - Systeme & Kabine
Standort: Oberpfaffenhofen
Institute & Einrichtungen:Institut für Robotik und Mechatronik > Systemdynamik und Regelungstechnik (war Entwurfsorientierte Regelungstechnik)
Hinterlegt von: Monika Klauer
Hinterlegt am:28 Apr 2010 14:54
Letzte Änderung:07 Feb 2013 21:00

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