Parameter identifiability under approximation
Authors:
K. Kunisch and L. W. White
Journal:
Quart. Appl. Math. 44 (1986), 475-486
MSC:
Primary 49D15; Secondary 93B30, 93C05
DOI:
https://doi.org/10.1090/qam/860900
MathSciNet review:
860900
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Abstract: The problem of injectivity of the parameter-to-state map is discussed for Galerkin approximations of a linear parabolic equation. A necessary and sufficient condition is derived and illustrated by means of simple examples. Finally, output least squares identifiability of the Galerkin approximations is discussed.
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A. Bamberger, G. Chavent, and P. Lailly, About the stability of the inverse problem in a 1-D wave equation—application to the interpretation of seismic profiles, J. Appl. Math. Optim. 5, 1–47 (1979)
H. T. Banks and P. L. Daniel, Estimation of variable coefficients in parabolic systems, LCDS Report 82-22, Brown University, Sept. 1982; IEEE Trans. Autom. Control. 30, 386–398 (1985)
H. T. Banks and K. Kunisch, An approximation theory for nonlinear partial differential equations with applications to identification and control, SIAM J. Control Optimization 20, 815–849 (1982)
G. Chavent, Local stability of the output least square parameter estimation technique, INRIA Report No. 136, Paris (1982); Mat. Apl. Comput. 2, 3–22 (1983)
I. M. Gelfand and B. M. Levitan, On the determination of a differential equation from its spectral function, Am. Math. Soc. Transl. 1, 253–304 (1955)
T. Kato, Perturbation theory for linear operators, Springer, New York, 1966
S. Kitamura and S. Nakagiri, Identifiability of spatially varying and constant parameters in distributed systems of parabolic type, SIAM J. Control Optimization 15, 785–802 (1979)
K. Kunisch and L. W. White, The parameter estimation problem for parabolic equations and discontinuous observation operators, SIAM J. Control Optimization 23, 900–927 (1985)
A. Pierce, Unique identification of eigenvalues and coefficients in a parabolic problem, SIAM J. Control Optimization 17, 494–499 (1979)
T. Suzuki, Uniqueness and nonuniqueness in an inverse problem for the parabolic equation, J. Differ. Eq. 47, 296–316 (1983)
L. W. White, Identification of a friction parameter in a first order linear hyperbolic equation, Proc. 22nd IEEE Conf. Decision and Control, San Antonio, 56–59 (1983)
A. E. Taylor and D. C. Lay, Introduction to functional analysis, Wiley, New York, 1980
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Article copyright:
© Copyright 1986
American Mathematical Society