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.
Item URL in elib: | https://elib.dlr.de/55646/ | ||||||
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Document Type: | Article | ||||||
Title: | On solving periodic Riccati equations | ||||||
Authors: |
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Date: | 2008 | ||||||
Journal or Publication Title: | Numerical Linear Algebra witih Applications | ||||||
Open Access: | Yes | ||||||
Gold Open Access: | No | ||||||
In SCOPUS: | No | ||||||
In ISI Web of Science: | No | ||||||
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 (old) | ||||||
DLR - Research area: | Aeronautics | ||||||
DLR - Program: | L AR - Aircraft Research | ||||||
DLR - Research theme (Project): | L - Systems & Cabin (old) | ||||||
Location: | Oberpfaffenhofen | ||||||
Institutes and Institutions: | Institute of Robotics and Mechatronics (until 2012) > System Dynamics and Control (former Control Design Engineering) | ||||||
Deposited By: | Klauer, Monika | ||||||
Deposited On: | 28 Oct 2008 | ||||||
Last Modified: | 31 Jul 2019 19:23 |
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