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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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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.

Titel:A numerical evaluation of solvers for the periodic Riccati differential equation
AutorenInstitution oder E-Mail-AdresseAutoren-ORCID
Gusev, SergeiSt. Petersburg State UniversityNICHT SPEZIFIZIERT
Johansson, StefanUmea UniversityNICHT SPEZIFIZIERT
Kagström, BoUmea UniversityNICHT SPEZIFIZIERT
Shiriaev, AntonNorwegian University of Science and TechnologyNICHT SPEZIFIZIERT
Varga, AndreasAndreas.Varga@dlr.deNICHT SPEZIFIZIERT
Datum:Februar 2010
Erschienen in:BIT Numerical Mathematics
Referierte Publikation:Ja
In Open Access:Nein
In ISI Web of Science:Ja
DOI :10.1007/s10543-010-0257-5
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 (alt)
DLR - Schwerpunkt:Luftfahrt
DLR - Forschungsgebiet:L AR - Starrflüglerforschung
DLR - Teilgebiet (Projekt, Vorhaben):L - Systeme & Kabine (alt)
Standort: Oberpfaffenhofen
Institute & Einrichtungen:Institut für Robotik und Mechatronik (bis 2012) > Systemdynamik und Regelungstechnik (war Entwurfsorientierte Regelungstechnik)
Hinterlegt von: Klauer, Monika
Hinterlegt am:28 Apr 2010 14:54
Letzte Änderung:07 Feb 2013 21:00

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