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On solving periodic Riccati equations

Varga, Andreas (2008) On solving periodic Riccati equations. Numerical Linear Algebra witih Applications, 15, pp. 809-835. Wiley InterScience. DOI: 10.1002/nla.604.

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Abstract

Numerically reliable algorithms to compute the periodic non-negative definite stabilizing solutions of the periodic differential Riccati equation (PRDE) and discrete-time periodic Riccati equation (DPRE) are proposed. For the numerical solution of PRDEs, a new multiple shooting-type algorithm is developed to compute the periodic solutions in an arbitrary number of time moments within one period by employing suitable discretizations of the continuous-time problems. In contrast to single shooting periodic generator methods, the multiple shooting-type methods have the main advantage of being able to address problems with larger periods. Three methods are discussed to solve DPREs. Two of the methods represetn extensions of a quotient-product swapping and collapsing "fast" algorithm. All proposed approches are completely general, being applicable to periodic Riccati equations with time-varying dimensions as well as with singular weighting matrices.

Document Type:Article
Title:On solving periodic Riccati equations
Authors:
AuthorsInstitution or Email of Authors
Varga, AndreasUNSPECIFIED
Date:2008
Journal or Publication Title:Numerical Linear Algebra witih Applications
Volume:15
DOI:10.1002/nla.604
Page Range:pp. 809-835
Publisher:Wiley InterScience
Status:Published
Keywords:periodic systems, periodic Riccati equations, periodic Lyapunov equations, periodic deadbeat control, numerical methods
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Aeronautics
HGF - Program Themes:Aircraft Research
DLR - Research area:Aeronautics
DLR - Program:L AR - Aircraft Research
DLR - Research theme (Project):L - Systems & Cabin
Location: Oberpfaffenhofen
Institutes and Institutions:Institute of Robotics and Mechatronics > System Dynamics and Control (former Control Design Engineering)
Deposited By: Monika Klauer
Deposited On:28 Oct 2008
Last Modified:12 Dec 2013 20:33

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