Identifiability of State Space Models: with applications to transformation systems

ISBN-13: 9783540115908 / Angielski / Miękka / 1982 / 216 str.

E. Walter

Opis

It is the objective of Science to formalize the relationships between observed quantities. The motivations of such a modelling procedure are varied, but can rougnly be collected around two pOles. If one is concerned with process control, one wants to find a model which wl11 De aDle to predlct tne process Denavlor, taKlng lnto account tne applled lnputs. The model will then be evaluated on it5 ability to mimic the ob5e ved input-output behavior under c: onditione; ae; vari"d ae; p

Spis treści

1. Transformation Systems.- 1.1 Introduction.- 1.2 Formalism.- 1.3 An example: nonlinear chemical kinetics.- 1.4 Specific problems of transformation system modelling.- 1.5 Conclusion.- 2. Structural Properties and Main Approaches to Checking Them.- 2.1 Introduction.- 2.2 Definitions.- 2.2.1 Structural properties and genericity.- 2.2.2 Connectability.- 2.2.3 Structural observabi1ity and structural controllability.- 2.2.4 Structural identifiability.- 2.2.5 Relations between these notions.- 2.3 Practical methods for checking structural observability and structural controllability of linear models.- 2.3.1 All nonzero entries are free.- 2.3.1.1 Graph theoretic approach.- 2.3.1.2 Algebraic approach.- 2.3.1.3 Conclusion.- 2.3.2 Nonzero entries are dependent.- 2.4 Main approaches to structural identifiability.- 2.4.1 Identifiable canonical representations.- 2.4.2 Global optimization.- 2.4.3 Berman and Schoonfold's approach.- 2.4.4 Transfer function approach.- 2.4.5 Minimal representation approach.- 2.4.6 Local approaches.- 2.4.7 Power series approach.- 2.4.8 Identifiability of large-scale linear models.- 2.5 Conclusion.- 3. Local Identifiability.- 3.1 Introduction.- 3.2 Methods.- 3.2.1 Use of the implicit function theorem.- 3.2.2 Local stability of identification algorithms.- 3.2.2.1 Newton and Gauss-Newton algorithms.- 3.2.2.2 Gauss-Seidel algorithm.- 3.2.2.3 Quasilinearization algorithm.- 3.2.3 Observability of the extended state.- 3.2.4 Information matrix.- 3.3 Linear models.- 3.4 Computer aided design of models.- 3.5 Implementation for linear transformation systems.- 3.5.1 Method A.- 3.5.2 Structural nature or the result obtained.- 3.5.3 Method B.- 3.5.4 Examples.- 3.6 Conclusion.- 4. Global Identifiability of Linear Models.- 4.1 Introduction.- 4.2 Properties of the transition matrix.- 4.3 Parametrization of the transition matrix.- 4.3.1 All the eigenvalues of A are real.- 4.3.2 Some eigenvalues of A are complex conjugates.- 4.3.3 Connection with Lagrange-Sylvester polynomials.- 4.4 Application to checking s.g. identifiability.- 4.4.1 The experimental data are entries of ?.- 4.4.1.1 No constraintexists on A.- 4.4.1.2 General procedure.- 4.4.1.3 Example: two-class transformation systems.- 4.4.2 Method for any B and C.- 4.4.3 Problems raised by inequality constraints.- 4.5 Conclusion.- 5. Exhaustive Modelling for Linear Models.- 5.1 Introduction.- 5.2 Class of the studied models.- 5.3 The matrices B and C are known.- 5. 3.1 The matrices B and C are standard.- 5.3.2 The matrices B and C are known, but non-standard.- 5.3.2.1 Standardization of CB.- 5.3.2.2 Standardization of B and C.- 5.4 The matrices B and C are partially unknown.- 5.5 Connections with Kalman's canonical form.- 5.6 Applications of exhaustive modelling.- 5.7 Conclusion.- 6. Examples.- 6.1 Introduction.- 6.2 Chemotherapeutic model.- 6.2.1 First experimental set-up.- 6.2.1.1 Connectabi1ity, structural observability and structural controllability.- 6.2.1.2 Structural local Identifiability.- 6.2.1.3 Exhaustive modelling.- 6.2.2 Second experimental set-up.- 6.2.2.1 Structural local identifiability.- 6.2.2.2 Exhaustive modelling.- 6.3 Hepatobiliary kinetics of B.S.P..- 6.3.1 Connectability, structural observability and structural controllability.- 6.3.2 Structural local identifiability.- 6.3.3 Exhaustive modelling.- 6.4 Metabolism of iodine.- 6.4.1 Structural local identifiability.- 6.4.2 Structural global identifiability.- 6.4.2.1 Input-output transformation.- 6.4.2.2 Standardization.- 6.4.2.3 Determination of AS.- 6.4.2.4 Introduction of the structural constraints on AS.- 6.5 Systemic distribution of Vincamine.- 6.6 Conclusion.- 7. Global Identifiability of Nonlinear Models.- 7.1 Introduction.- 7.2 Series expansion approach.- 7.2.1 Time-power series.- 7.2.2 Generating series.- 7.3 Linearization approach.- 7.3.1 Principle.- 7.3.2 Application to nonlinear transformation systems.- 7.3.2.1 Physical linearization by tracer inclusion.- 7.3.2.2 Mathematical linearization.- 7.3.2.3 What is the best linearization?.- 7.3.3 Generalization.- 7.4 Conclusion.- Conclusion.- References.