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Strong convergence and convergence rates of approximating solutions for algebraic Riccati equations in Hilbert spacesThe linear quadratic optimal control problem on infinite time interval for linear time-invariant systems defined on Hilbert spaces is considered. The optimal control is given by a feedback form in terms of solution pi to the associated algebraic Riccati equation (ARE). A Ritz type approximation is used to obtain a sequence pi sup N of finite dimensional approximations of the solution to ARE. A sufficient condition that shows pi sup N converges strongly to pi is obtained. Under this condition, a formula is derived which can be used to obtain a rate of convergence of pi sup N to pi. The results of the Galerkin approximation is demonstrated and applied for parabolic systems and the averaging approximation for hereditary differential systems.
Document ID
19870014689
Acquisition Source
Legacy CDMS
Document Type
Contractor Report (CR)
Authors
Ito, Kazufumi (Brown Univ., Providence R. I., United States)
Date Acquired
September 5, 2013
Publication Date
May 1, 1987
Subject Category
Cybernetics
Report/Patent Number
NASA-CR-178302
NAS 1.26:178302
ICASE-87-31
AD-A192764
Accession Number
87N24122
Funding Number(s)
CONTRACT_GRANT: NAS1-18107
CONTRACT_GRANT: AF-AFOSR-0398-84
PROJECT: RTOP 505-90-21-01
CONTRACT_GRANT: AF-AFOSR-0303-85
CONTRACT_GRANT: NAS1-17070
CONTRACT_GRANT: NAG1-517
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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