Introduction / 1: |
New Challenges for System Identification / 1.1: |
The Birth of LPV Systems / 1.2: |
The Present State of LPV Identification / 1.3: |
The Identification Cycle / 1.3.1: |
General Picture of LPV Identification / 1.3.2: |
LPV-Io Representation Based Methods / 1.3.3: |
LPV-SS Representation Based Methods / 1.3.4: |
Similarity to Other System Classes / 1.3.5: |
Challenges and Open Problems / 1.4: |
Perspectives of Orthonormal Basis Function Models / 1.5: |
The Gain-Scheduling Perspective / 1.5.1: |
The Global Identification Perspective / 1.5.2: |
Approximation via OBF Structures / 1.5.3: |
The Goal of the Book / 1.6: |
Overview of Contents / 1.7: |
LTI System Identification and the Role of OBFs / 2: |
The Concept of Orthonormal Basis Functions / 2.1: |
Signal Spaces and Inner Functions / 2.2: |
General Class of Orthonormal Basis Functions / 2.3: |
Takenaka-Malmquist Basis / 2.3.1: |
Hambo Basis / 2.3.2: |
Kautz Basis / 2.3.3: |
Laguerre Basis / 2.3.4: |
Pulse Basis / 2.3.5: |
Orthonormal Basis Functions of MIMO Systems / 2.3.6: |
Basis Functions in Continuous-Time / 2.3.7: |
Modeling and Identification of LTI Systems / 2.4: |
The Identification Setting / 2.4.1: |
Model Structures / 2.4.2: |
Properties / 2.4.3: |
Linear Regression / 2.4.4: |
Identification with OBFs / 2.4.5: |
Pole Uncertainty of Model Estimates / 2.4.6: |
Validation in the Prediction-Error Setting / 2.4.7: |
The Kolmogorov n-Width Theory / 2.5: |
Conclusions / 2.6: |
LPV Systems and Representations / 3: |
General Class of LPV Systems / 3.1: |
Parameter Varying Dynamical Systems / 3.1.1: |
Representations of Continuous-Time LPV Systems / 3.1.2: |
Representations of Discrete-Time LPV Systems / 3.1.3: |
Equivalence Classes and Relations / 3.2: |
Equivalent Kernel Representations / 3.2.1: |
Equivalent IO Representations / 3.2.2: |
Equivalent State-Space Representations / 3.2.3: |
Properties of LPV Systems and Representations / 3.3: |
State-Observability and Reachability / 3.3.1: |
Stability of LPV Systems / 3.3.2: |
Gramians of LPV State-Space Representations / 3.3.3: |
LPV Equivalence Transformations / 3.4: |
State-Space Canonical Forms / 4.1: |
The Observability Canonical Form / 4.1.1: |
Reachability Canonical Form / 4.1.2: |
Companion Canonical Forms / 4.1.3: |
Transpose of SS Representations / 4.1.4: |
LTI vs. LPV State Transformation / 4.1.5: |
From State-Space to the Input-Output Domain / 4.2: |
From the Input-Output to the State-Space Domain / 4.3: |
The Idea of Recursive State-Construction / 4.3.1: |
Cut-and-Shift in Continuous-Time / 4.3.2: |
Cut-and-Shift in Discrete-Time / 4.3.3: |
State-Maps and Polynomial Modules / 4.3.4: |
State-Maps Based on Kernel Representations / 4.3.5: |
State-Maps Based on Image-Representations / 4.3.6: |
State-Construction in the MIMO Case / 4.3.7: |
LPV Series-Expansion Representations / 4.4: |
Relevance of Series-Expansion Representations / 5.1: |
Impulse Response Representation of LPV Systems / 5.2: |
Filter Form of LPV-IO Representations / 5.2.1: |
Series Expansion in the Pulse Basis / 5.2.2: |
The Impulse Response Representation / 5.2.3: |
LPV Series Expansion by OBFs / 5.3: |
The OBF Expansion Representation / 5.4: |
Series Expansions and Gain-Scheduling / 5.5: |
The Role of Gain-Scheduling / 5.5.1: |
Optimality of the Basis in the Frozen Sense / 5.5.2: |
Optimality of the Basis in the Global Sense / 5.5.3: |
Discretization of LPV Systems / 5.6: |
The Importance of Discretization / 6.1: |
Discretization of LPV System Representations / 6.2: |
Discretization of State-Space Representations / 6.3: |
Complete Method / 6.3.1: |
Approximative State-Space Discretization Methods / 6.3.2: |
Discretization Errors and Performance Criteria / 6.4: |
Local Discretization Errors / 6.4.1: |
Global Convergence and Preservation of Stability / 6.4.2: |
Guaranteeing a Desired Level of Discretization Error / 6.4.3: |
Switching Effects / 6.4.4: |
Properties of the Discretization Approaches / 6.5: |
Discretization and Dynamic Dependence / 6.6: |
Numerical Example / 6.7: |
LPV Modeling of Physical Systems / 6.8: |
Towards Model Structure Selection / 7.1: |
General Questions of LPV Modeling / 7.2: |
Modeling of Nonlinear Systems in the LPV Framework / 7.3: |
First Principle Models / 7.3.1: |
Linearization Based Approximation Methods / 7.3.2: |
Multiple Model Design Procedures / 7.3.3: |
Substitution Based Transformation Methods / 7.3.4: |
Automated Model Transformation / 7.3.5: |
Summary of Existing Techniques / 7.3.6: |
Translation of First Principle Models to LPV Systems / 7.4: |
Problem Statement / 7.4.1: |
The Transformation Algorithm / 7.4.2: |
Handling Non-Factorizable Terms / 7.4.3: |
Properties of the Transformation Procedure / 7.4.4: |
Optimal Selection of OBFs / 7.5: |
Perspectives of OBFs Selection / 8.1: |
Kolmogorov n-Width Optimality in the Frozen Sense / 8.2: |
The Fuzzy-Kolmogorov c-Max Clustering Approach / 8.3: |
The Pole Clustering Algorithm / 8.3.1: |
Properties of the FKcM / 8.3.2: |
Simulation Example / 8.3.3: |
Robust Extension of the FKcM Approach / 8.4: |
Questions of Robustness / 8.4.1: |
Basic Concepts of Hyperbolic Geometry / 8.4.2: |
Pole Uncertainty Regions as Hyperbolic Objects / 8.4.3: |
The Robust Pole Clustering Algorithm / 8.4.4: |
Properties of the Robust FKcM / 8.4.5: |
LPV Identification via OBFs / 8.4.6: |
Aim and Motivation of an Alternative Approach / 9.1: |
OBFs Based LPV Model Structures / 9.2: |
The LPV Prediction-Error Framework / 9.2.1: |
The Wiener and the Hammerstein OBF Models / 9.2.2: |
Properties of Wiener and Hammerstein OBF Models / 9.2.3: |
OBF Models vs. Other Model Structures / 9.2.4: |
Identification of W-LPV and H-LPV OBF Models / 9.2.5: |
Identification with Static Dependence / 9.3: |
LPV Identification with Fixed OBFs / 9.3.1: |
Local Approach / 9.3.3: |
Global Approach / 9.3.4: |
Examples / 9.3.5: |
Approximation of Dynamic Dependence / 9.4: |
Feedback-Based OBF Model Structures / 9.4.1: |
Properties of Wiener and Hammerstein Feedback Models / 9.4.2: |
Identification by Dynamic Dependence Approximation / 9.4.3: |
Example / 9.4.4: |
Extension towards MIMO Systems / 9.5: |
Scalar Basis Functions / 9.5.1: |
Multivariable Basis Functions / 9.5.2: |
Multivariable Basis Functions in the Feedback Case / 9.5.3: |
General Remarks on the MIMO Extension / 9.5.4: |
Proofs / 9.6: |
Proofs of Chapter 3 / A.1: |
The Injective Cogenerator Property / A.1.1: |
Existence of Full Row Rank KR Representation / A.1.2: |
Elimination Property / A.1.3: |
State-Kernel Form / A.1.4: |
Left/Right-Side Unimodular Transformation / A.1.5: |
Proofs of Chapter 5 / A.2: |
LPV Series Expansion, Pulse Basis / A.2.1: |
LPV Series Expansion, OBFs / A.2.2: |
Proofs of Chapter 8 / A.3: |
Optimal Partition / A.3.1: |
h-Center Relation / A.3.2: |
h-Segment Worst-Case Distance / A.3.4: |
h-Disc Worst-Case Distance / A.3.6: |
Convexity / A.3.7: |
Optimal Robust Partition / A.3.8: |
Proofs of Chapter 9 / A.4: |
Representation of Dynamic Dependence / A.4.1: |
References |
Index |
Introduction / 1: |
New Challenges for System Identification / 1.1: |
The Birth of LPV Systems / 1.2: |