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Shifting the closed-loop spectrum in the optimal linear quadratic regulator problem for hereditary systemsIn the optimal linear quadratic regulator problem for finite dimensional systems, the method known as an alpha-shift can be used to produce a closed-loop system whose spectrum lies to the left of some specified vertical line; that is, a closed-loop system with a prescribed degree of stability. This paper treats the extension of the alpha-shift to hereditary systems. As infinite dimensions, the shift can be accomplished by adding alpha times the identity to the open-loop semigroup generator and then solving an optimal regulator problem. However, this approach does not work with a new approximation scheme for hereditary control problems recently developed by Kappel and Salamon. Since this scheme is among the best to date for the numerical solution of the linear regulator problem for hereditary systems, an alternative method for shifting the closed-loop spectrum is needed. An alpha-shift technique that can be used with the Kappel-Salamon approximation scheme is developed. Both the continuous-time and discrete-time problems are considered. A numerical example which demonstrates the feasibility of the method is included.
Document ID
19870065448
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
Authors
Gibson, J. S.
(California, University Los Angeles, United States)
Rosen, I. G.
(Southern California, University Los Angeles, CA, United States)
Date Acquired
August 13, 2013
Publication Date
September 1, 1987
Publication Information
Publication: IEEE Transactions on Automatic Control
Volume: AC-32
ISSN: 0018-9286
Subject Category
Cybernetics
Accession Number
87A52722
Funding Number(s)
CONTRACT_GRANT: NAS1-17070
CONTRACT_GRANT: AF-AFOSR-84-0393
CONTRACT_GRANT: AF-AFOSR-84-0309
Distribution Limits
Public
Copyright
Other

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