Realization and Model Reduction of Dynamical Systems : A Festschrift in Honor of the 70th Birthday of Thanos Antoulas

This book celebrates Professor Thanos Antoulas's 70th birthday, marking his fundamental contributions to systems and control theory, especially model reduction and, more recently, data-driven modeling and system identification. Model reduction is a prominent research topic with wide ranging scientific and engineering applications. Rational and Systematic—A Mathematical Biography of Thanos Antoulas Contents Linear Dynamical Systems The Rational Interpolation Problem: Grassmannian and Loewner-Matrix Approaches 1 Introduction 2 Review of the Grassmannian Approach to Rational Interpolation 2.1 Parametrization of Interpolants with Prescribed Macmillan Degree 2.2 Nevanlinna-Pick Interpolation 3 Other Several-Variable Generalizations: Free Noncommutative Rational Functions 3.1 Noncommutative Polynomials 3.2 Noncommutative Rational Matrix Functions 4 Conclusion References The Conditioning of a Linear Barycentric Rational Interpolant 1 Introduction 2 The Conditioning of the Interpolant R1 2.1 Equidistant Nodes 2.2 Well-Spaced Nodes 2.3 Conformally Shifted Nodes 3 Conclusion References Learning Low-Dimensional Dynamical-System Models from Noisy Frequency-Response Data with Loewner Rational Interpolation 1 Introduction 2 Learning Low-Dimensional Dynamical-System Models with Loewner Rational Interpolation 2.1 Linear Time-Invariant Dynamical Systems 2.2 Loewner Rational Interpolation 3 Learning Loewner Models from Noisy Frequency-Response Measurements 3.1 Noisy Transfer-Function Values 3.2 Loewner and Noisy Transfer-Function Values 3.3 Noise Structure 3.4 Bounding the Error Due to Noisy Transfer-Function Values 3.5 Remarks on Theorem 1 4 Numerical Results 4.1 CD Player 4.2 Penzl References Pseudospectra of Loewner Matrix Pencils 1 Introduction 2 Loewner Realization Theory in a Nutshell 2.1 Selecting and Arranging Interpolation Points 2.2 Construction of Interpolants 3 Pseudospectra for Matrix Pencils 4 Efficient Computation of Loewner Pseudospectra 5 Example 1: Eigenvalue Sensitivity and Transient Behavior 6 Example 2: Partitioning Interpolation Points and Noisy Data 7 Conclusion References A Loewner Matrix Approach to the Identification of Linear Time-Varying Systems 1 Introduction 2 Problem Statement 3 A Loewner Matrix for Time-Varying Systems 3.1 Relation with the Classical Loewner Matrix 4 Properties of the Time-Varying Loewner Matrix 4.1 Relation with the Time-Invariant Case 5 From Loewner Matrix to State Equations 6 Conclusions and Ongoing Research References Linear System Matrices of Rational Transfer Functions 1 Introduction 2 Background 3 Strong Irreducibility and Minimality 4 Reducing to a Strongly Minimal Linear System Matrix 5 Computational Aspects 6 Numerical Results 7 Conclusion References Nonlinear Dynamical Systems Interpolation-Based Model Order Reduction for Quadratic-Bilinear Systems and mathcalH2 Optimal Approximation 1 Introduction 2 Generalized Transfer Functions and the mathcalH2 Norm 2.1 Pole-Residue Representation of the Generalized Transfer Functions 3 Volterra Series Interpolation and mathcalH2 Optimal Approximation 3.1 Volterra Series Interpolation 3.2 mathcalH2 Optimal Approximation 3.3 Computational Aspects 4 Numerical Examples 4.1 Fisher-KPP Equation 5 Conclusions References An Adaptive Sampling Approach for the Reduced Basis Method 1 Introduction 2 Reduced Basis Method 3 Adaptive Parameter Sampling 3.1 Radial Basis Functions 3.2 POD-Greedy Algorithm with Adaptive Sampling 3.3 A Fully Adaptive POD-Greedy-(D)EIM Algorithm 3.4 A Strategy for Shape Parameter Selection 4 Numerical Results 4.1 Burgers' Equation 4.2 Convection-Diffusion Equation 4.3 A Thermal Model 5 Conclusion References Balanced Truncation Model Reduction for Lifted Nonlinear Systems 1 Introduction 2 Quadratic-Bilinear Systems and Balancing 3 Lifting Systems to QB Form: Introducing Structure 3.1 Structure in Lifted QB Systems 3.2 Tubular Reactor Model 4 Balancing for Lifted Systems with Special Structure 4.1 Artificial Stabilization 4.2 Balancing with Gramians of Linearized System 4.3 Balancing with Truncated (Quadratic) Gramians 5 Numerical Results 6 Conclusions References Modeling the Buck Converter from Measurements of Its Harmonic Transfer Function 1 Introduction 2 Modeling Periodic Systems in the Frequency Domain 2.1 Linear Time-Invariant Systems in the Frequency Domain 2.2 Periodic Systems in the Frequency Domain 3 Review of the Loewner Framework 4 Analysis of the Buck Converter as a PSL System 4.1 Ideal System 4.2 Integrating the ON Resistance of the Semiconductor Devices 4.3 Numerical Experiments 5 Conclusion and Future Work References Model Reduction and Realization Theory of Linear Switched Systems 1 Introduction 2 Linear Switched Systems: Basic Definitions 3 Realization Theory of Linear Switched Systems 3.1 Minimality of Linear Switched Systems 3.2 Existence of a Realization, Ho-Kalman Algorithm, Markov Parameters 4 Model Reduction 4.1 Model Reduction by Balanced Truncation 4.2 Moment Matching 5 Conclusions References Structured Dynamical Systems Developments in the Computation of Reduced Order Models with the Use of Dominant Spectral Zeros 1 Introduction 2 Spectral Zeros and Model Order Reduction 3 Variant for Computing Dominant Spectral Zeros 4 The Impact of D Term Size on DSZ Numerical Computations 5 Electrical Circuits 5.1 Dynamic Modeling 5.2 Results of Experiments 5.3 Experiments on Circuits with Many PI Sections 6 Experiments on an Actual Power System Model 7 Conclusion References Structure-Preserving Interpolatory Model Reduction for Port-Hamiltonian Differential-Algebraic Systems 1 Introduction 2 General Differential-Algebraic Systems 3 Regularization of PHDAE Systems 4 Interpolatory Model Reduction of pHDAEs 4.1 Semi-explicit Index-1 pHDAE Systems 4.2 Semi-explicit pHDAE Systems with Index-2 Constraints 4.3 Semi-explicit pHDAE Systems with Index-1 and Index-2 Constraints 5 Algorithmic Considerations 5.1 mathcalH2 -inspired Structure-Preserving Interpolation 5.2 Numerical Example 6 Conclusions References Data-Driven Identification of Rayleigh-Damped Second-Order Systems 1 Introduction 2 Classical Loewner Framework 3 Second-Order Loewner Framework 3.1 Second-Order Loewner Matrices 3.2 Identification of Rayleigh-Damped Second-Order Systems 3.3 Optimizing Parameters 3.4 A Note on More General Damping Structures 4 Numerical Results 4.1 Demo Example 4.2 Building Example 4.3 Artificial Fishtail 5 Conclusions References Balanced Truncation Model Reduction for 3D Linear Magneto-Quasistatic Field Problems 1 Introduction 2 Model Problem 2.1 FEM Discretization 3 Properties of the FEM Model 3.1 Regularization 3.2 Stability 3.3 Passivity 4 Balanced Truncation Model Reduction 5 Computational Aspects 6 Numerical Results References Structure-Preserving Model Reduction of Physical Network Systems 1 Introduction 2 A Class of Linear Physical Network Systems 3 Structure-Preserving Model Reduction by Clustering 4 Structure-Preserving Model Reduction by Kron Reduction 5 Steady State Equivalence of the Full and Reduced Order Model 6 Structure-Preserving Model Reduction of Chemical Reaction Networks 6.1 The Canonical Representation of Detailed-Balanced Mass Action Kinetics Reaction Networks 6.2 Structure-Preserving Model Reduction by Clustering 6.3 Structure Preserving Model Reduction by Kron Reduction 7 Conclusions and Outlook References Model Reduction for Control mathcalH2-gap Model Reduction for Stabilizable and Detectable Systems 1 Introduction 2 Left-Coprime Factorizations and the Gap Metric 3 mathcalH2-gap Model Reduction 3.1 Pole-Residue Formulae for the mathcalH2-gap Measure 3.2 mathcalH2-gap Formula and Interpolation. 3.3 Model Reduction with Respect to the mathcalH 2-gap Measure 3.4 Algorithm 1 and mathcalH 2-gap Optimality. 4 Numerical Examples 4.1 An Unstable Convection Diffusion Equation 4.2 Linearized Navier-Stokes Equations 5 Conclusion References Reduced Order Model Hessian Approximations in Newton Methods for Optimal Control 1 Introduction 2 Inexact Newton Methods and ROM Hessian Approximations 3 ROM Hessian Approximations for Discrete Time Optimal Control Problems 4 Numerical Results 5 Conclusions References Interpolation-Based Irrational Model Control Design and Stability Analysis 1 Introduction and Problem Statement 1.1 Motivations for Interpolation as a Pivotal Tool and Driving Example 1.2 Problem Statement, Contribution and Organisation 1.3 Notations and Preliminaries 2 Background on Data-Driven LTI Model Approximation 2.1 LTI Dynamical Models and Input-Output Data 2.2 Data-Driven Approximation and Loewner Framework at a Glance 3 Model- and Data-Driven Control Synthesis Paradigm 3.1 Model-Driven Approximation and Control 3.2 Data-Driven Control 3.3 Model- Vs. Data-Driven Control Design Remarks 4 Stability Assessment of mathcalL2 Meromorphic Functions 4.1 The mathcalLinfty Procedure 4.2 Approximation-Driven Arguments for the mathcalLinfty-MFSA 5 Conclusion References Applications Oscillations in Biology 1 Cycles in Biology 1.1 Introduction 1.2 Krebs Cycle in Biological Systems for Energy Generation 1.3 Essential Biological Rhythms 1.4 Molecular Oscillators 2 Mathematical Tools for Biological Oscillation Discovery 2.1 Introduction 2.2 Matrix Pencil Method for Studying Oscillations in Transcription 2.3 Difficulty in Data Assessment and Analysis of Oscillation in Biological Data 3 Conclusion References Model-Order Reduction for Coupled Flow and Linear Thermal-Poroplasticity with Applications to Unconventional Reservoirs 1 Introduction 2 Mathematical Model for Thermo-Poroelasticity 2.1 Discretization of the Flow Equations 3 Proposed MOR Method 3.1 Global MOR Algorithm 3.2 Global-in-Time POD Algorithm (GPOD) 3.3 Two-Step Global-in-Time DEIM (GDEIM) Process 4 Numerical Example 4.1 Example: Two-Phase Flow in an Unconventional RS 5 Conclusions References Challenges in Model Reduction for Real-Time Simulation of Traction Chain Systems 1 Introduction 2 Fundamentals of Real-Time Simulation 3 Discrete-Time Simulation 3.1 Numerical Integration 4 Model Order Reduction in Switched-Linear Systems 4.1 Dominant Poles and Moment Matching at DC 4.2 Reinserting Reduced-Order Models in Simulations 5 Experiments 5.1 Dominant Pole Matching 5.2 Dominant Pole and DC Moment Matching 5.3 Reduction in Execution Time 6 Conclusion References Sparse Representation for Sampled-Data Hinfty Filters 1 Introduction 2 Problem Formulation 3 Sparse FIR Filter Design via Sampled-Data Hinfty Optimization 4 Extension to Multi-rate Filters 5 Example: Analog Filter Discretization 6 Application to Delta-Sigma Modulator Design 7 Conclusion References Analysis of a Reduced Model of Epithelial–Mesenchymal Fate Determination in Cancer Metastasis as a Singularly-Perturbed Monotone System 1 Introduction 2 Modeling of the EMT/MET System 2.1 Promoter Dynamics 2.2 RNA Dynamics 2.3 Slow Dynamics 3 Monotone Systems and Singular Perturbations 3.1 Monotone Systems 3.2 Graphical Characterization of Monotonicity 3.3 Singular Perturbation Model Reduction 4 Analysis of the Core EMT/MET Network 4.1 Stability of the Fast Dynamics 4.2 Monotonicity of the Reduced System 4.3 Remarks on Generic Convergence for Singularly Perturbed Monotone Systems 5 Conclusions References