Ebook: Estimation Techniques for Distributed Parameter Systems

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.2.1. Modal Approximations.- III.2.2. Cubic Spline Approximations.- 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.5.1. Theory.- IV.5.2. Applications.- IV.6. Output Least Squares Stability.- IV.6.1. Theory.- IV.6.2. An Example.- IV.7. Regularization.- IV.7.1. Tikhonov’s Lemma and Its Application.- IV.7.2. Regularization Revisited.- IV.8. Concluding Remarks on Stability.- IV.8.1. A Summary of Possible Approaches.- IV.8.2. Remarks on Implementation.- 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.4.1. Method of Characteristics.- VI.4.2. Equation Error Method.- VI.4.3. A Variational Technique.- VI.4.4. Singular Perturbation Techniques.- VI.4.5. Adaptive Control Methods.- VI.4.6. An Augmented Lagrangian Technique.- VI.5. Numerical Test Examples.- VII An Annotated Bibliography.- Al) Preliminaries.- A2) Linear Splines.- A3) Cubic Hermite Splines.- A5) Polynomial Splines, Quasi- Interpolation.