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Estimation Techniques for Distributed Parameter Systems

Author: H T Banks; K Kunisch
Publisher: Boston, MA : Birkhäuser Boston, 1989.
Series: Systems & control.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
The research detailed in this monograph was originally motivated by our interest in control problems involving partial and delay differential equations. Our attempts to apply control theory techniques to such prob lems in several areas of science convinced us that in the need for better and more detailed models of distributed/ continuum processes in biology and mechanics lay a rich, interesting, and challenging  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: H T Banks; K Kunisch
ISBN: 9781461237006 1461237009
OCLC Number: 852789183
Description: 1 online resource (volumes).
Contents: I Examples of Inverse Problems Arising in Applications --
I.1. Inverse Problems in Ecology --
I.2. Inverse Problems in Lake and Sea Sedimentation Analysis --
I.3. Inverse Problems in the Study of Flexible Structures --
I.4. Inverse Problems in Physiology --
II Operator Theory Preliminaries --
II. 1. Linear Semigroups --
II. 2. Galerkin Schemes --
III Parameter Estimation: Basic Concepts and Examples --
III. 1. The Parameter Estimation Problem --
III. 2. Application of the Theory to Special Schemes for Linear Parabolic Systems --
III. 3. Parameter Dependent Approximation and the Nonlinear Variation of Constants Formula --
IV Identifiability and Stability --
IV. 1. Generalities --
IV. 2. Examples --
IV. 3. Identifiability and Stability Concepts --
IV. 4. A Sufficient Condition for Identifiability --
IV. 5. Output Least Squares Identifiability --
IV. 6. Output Least Squares Stability --
IV. 7. Regularization --
IV. 8. Concluding Remarks on Stability --
V Parabolic Equations --
V.1. Modal Approximations: Discrete Fit-to-Data Criteria --
V.2. Quasimodal Approximations --
V.3. Operator Factorization: A = -C*C --
V.4. Operator Factorization: A = A1/2A1/2 --
V.5. Numerical Considerations --
V.6. Numerical Test Examples --
V.7. Examples with Experimental Data --
VI Approximation of Unknown Coefficients in Linear Elliptic Equations --
VI. 1. Parameter Estimation Convergence --
VI. 2. Function Space Parameter Estimation Convergence --
VI. 3. Rate of Convergence for a Special Case --
VI. 4. Methods Other Than Output-Least-Squares --
VI. 5. Numerical Test Examples --
VII An Annotated Bibliography --
Al) Preliminaries --
A2) Linear Splines --
A3) Cubic Hermite Splines --
A5) Polynomial Splines, Quasi- Interpolation.
Series Title: Systems & control.
Responsibility: by H.T. Banks, K. Kunisch.

Abstract:

The research detailed in this monograph was originally motivated by our interest in control problems involving partial and delay differential equations.  Read more...

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