Identifiability of State Space Models

with applications to transformation systems
Softcover Nachdruck of the original 1. Auflage 1982
ISBN: 978-3-540-11590-8
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 46, 216 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 335 g

Reihe: Lecture Notes in Biomathematics

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

Zielgruppe

Research

Autoren/Hrsg.

Walter, E.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Naturwissenschaften Biowissenschaften Angewandte Biologie Biomathematik

Inhaltsverzeichnis

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.