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Parameter estimation in nonlinear distributed systems - Approximation theory and convergence resultsAn abstract approximation framework and convergence theory is described for Galerkin approximations applied to inverse problems involving nonlinear distributed parameter systems. Parameter estimation problems are considered and formulated as the minimization of a least-squares-like performance index over a compact admissible parameter set subject to state constraints given by an inhomogeneous nonlinear distributed system. The theory applies to systems whose dynamics can be described by either time-independent or nonstationary strongly maximal monotonic operators defined on a reflexive Banach space which is densely and continuously embedded in a Hilbert space. It is demonstrated that if readily verifiable conditions on the system's dependence on the unknown parameters are satisfied, and the usual Galerkin approximation assumption holds, then solutions to the approximating problems exist and approximate a solution to the original infinite-dimensional identification problem.
Document ID
19890051477
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
Authors
Banks, H. T.
(Brown University Providence, RI, United States)
Reich, Simeon
(Southern California, University Los Angeles, CA; Technion - Israel Institute of Technology, Haifa, United States)
Rosen, I. G.
(Southern California, University Los Angeles, CA, United States)
Date Acquired
August 14, 2013
Publication Date
January 1, 1988
Publication Information
Publication: Applied Mathematics Letters
Volume: 1
Issue: 3 19
ISSN: 0893-9659
Subject Category
Numerical Analysis
Accession Number
89A38848
Funding Number(s)
CONTRACT_GRANT: AF-AFOSR-84-0393
CONTRACT_GRANT: F49620-86-C-0111
CONTRACT_GRANT: NSF MCS-85-04316
CONTRACT_GRANT: NAS1-18107
CONTRACT_GRANT: AF-AFOSR-87-0356
CONTRACT_GRANT: NAG1-517
CONTRACT_GRANT: AF-AFOSR-84-0398
CONTRACT_GRANT: NAS1-17070
Distribution Limits
Public
Copyright
Other

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