Identifiability of State Space Models: with applications to transformation systems

by E. Walter

Overview

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; po

Product Details

ISBN-13:	9783540115908
Publisher:	Springer Berlin Heidelberg
Publication date:	10/01/1982
Series:	Lecture Notes in Biomathematics , #46
Edition description:	Softcover reprint of the original 1st ed. 1982
Pages:	216
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

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.- 2.3 Practical methods for checking structural observability and structural controllability of linear models.- 2.4 Main approaches to structural identifiability.- 2.5 Conclusion.- 3. Local Identifiability.- 3.1 Introduction.- 3.2 Methods.- 3.3 Linear models.- 3.4 Computer aided design of models.- 3.5 Implementation for linear transformation systems.- 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.- 4.4 Application to checking s.g. identifiability.- 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.- 5.4 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.- 6.3 Hepatobiliary kinetics of B.S.P..- 6.4 Metabolism of iodine.- 6.5 Systemic distribution of Vincamine.- 6.6 Conclusion.- 7. Global Identifiability of Nonlinear Models.- 7.1 Introduction.- 7.2 Series expansion approach.- 7.3 Linearization approach.- 7.4 Conclusion.- Conclusion.- References.