Identifiability of Parametric Models

TutorialChapter 1: Identifiability of Model Parameters 1 Introduction 2 Basic concepts and Identifiability Analysis for Noise-Free Linear Time-Invariant Models 2.1 Basic Concepts and Linear Models 2.2 The Laplace Transform or Transfer Function Approach 2.3 Taylor Series Expansion of the Observations 2.4 Markov Parameter Matrix Approach 2.5 Modal Matrix Approach 2.6 Exhaustive Modeling Approach 2.7 Discussion and Other Problems 3 Complete Models, General Definitions and Nonlinear Systems 3.1 Complete Models and General Definitions 3.3 Identifiability Analysis of Nonlinear Models: The Taylor Series Approach 3.4 Discussion 4 Parameter Bounds for Unidentifiable Linear Models 4.1 Interval Analysis: An Alternative to Multiinput-Multioutput Experiments 4.2 Compartmental Models 4.3 Two-Compartment System 4.4 Three-Compartment Mammillary System 4.5 Discussion 5 Numerical Identifiability: Is this Really a New Problem? 6 Concluding Remarks ReferencesLinear ModelsChapter 2: Results and Conjectures on the Identifiability of Linear Systems 1 Introduction 2 Equations Derived from Experimental Data 2.1 Equations for the Evolution of Linear Models 2.2 Equations for the Identifiability Problem 3 Results on Local Identifiability 3.1 Introduction 3.2 Construction of Matrix K 3.3 Principle of the Method 3.4 Main Results 4 A Particular Result on Global Identifiability 4.1 Introduction 4.2 A Simple Example 4.3 Use of the Norm-Coerciveness Theorem 4.4 Conjectures on Global Identifiability 5 Examples of the Application of Conjecture 1 6 Examples of the Application of Conjecture 2 7 Conclusion ReferencesChapter 3: On Structural Equivalence and Identifiability Constraint Ordering 1 Introduction 2 Mathematical Background 3 Structural Equivalence 4 Exhaustive Modeling References AppendixNonlinear and Time-Varying ModelsChapter 4: Identifiability of Polynomial Systems: Structural and Numerical Aspects 1 Introduction 2 Deterministic Identifiability: Problem Statement 3 Algebraic Invariants for Homogeneous Polynomial Models 4 Analysis of Deterministic Identifiability 5 Practical Identifiability: Problem Statement 6 Principal Component Analysis of Practical Identifiability 7 A Case Study on Methane Pyrolysis 8 Conclusions ReferencesChapter 5: Volterra and Generating Power Series Approaches to Identifiability Testing 1 Introduction 2 Problem Statement 3 Generating Series Approach 3.1 Iterated Integrals 3.2 Analytic Causal Functionals and Generating Power Series 3.3 A First Method for Computing Terms of a gps 3.4 Identifiability Testing with gps 3.5 A Second Method for Computing a gps 4 Volterra Series Approach 4.1 Volterra Series and Differential Operators 4.2 A Third Method for Computing Terms of a gps 4.3 Identifiability Testing 5 Conclusions ReferencesInfinite-Dimensional ModelsChapter 6: Identifiability of Parameters in the Output Least Square Formulation 1 Introduction 2 A Sufficient Condition for OLSI 3 Finite Dimensional Parameters 4 A Weaker Condition on the Derivative 5 OLS-Identifiability by Regularization ReferencesComputer AlgebraChapter 7: The Testing of Structural Properties Through Symbolic Computation 1 Introduction 2 Definitions and Problem Statement 3 Jacobian Matrix and Global Injectivity 4 Methods for Testing Structural Controllability and Structural Observability 5 Methods for Testing Structural Identifiability 6 Methods for Testing Structural Distinguishability 7 Solution of a Set of Polynomial Equations 7.