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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
19860015696
Acquisition Source
Legacy CDMS
Document Type
Contractor Report (CR)
Authors
Gibson, J. S. (NASA Langley Research Center Hampton, VA, United States)
Rosen, I. G. (NASA Langley Research Center Hampton, VA, United States)
Date Acquired
September 5, 2013
Publication Date
March 1, 1985
Subject Category
Cybernetics
Report/Patent Number
NAS 1.26:178082
NASA-CR-178082
ICASE-86-16
Report Number: NAS 1.26:178082
Report Number: NASA-CR-178082
Report Number: ICASE-86-16
Accession Number
86N25167
Funding Number(s)
CONTRACT_GRANT: AF-AFOSR-0393-84
CONTRACT_GRANT: AF-AFOSR-0309-84
CONTRACT_GRANT: NAS1-18107
CONTRACT_GRANT: NAS1-17070
PROJECT: RTOP 505-31-83-01
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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