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Hybrid system identification : theory and algorithms for learning switching models

Author: Fabien Lauer; Gérard Bloch
Publisher: Cham : Springer, 2018. ©2019
Series: Lecture notes in control and information sciences, 478.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
Hybrid System Identification helps readers to build mathematical models of dynamical systems switching between different operating modes, from their experimental observations. It provides an overview of the interaction between system identification, machine learning and pattern recognition fields in explaining and analysing hybrid system identification. It emphasises the optimization and computational complexity  Read more...
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Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Fabien Lauer; Gérard Bloch
ISBN: 9783030001933 3030001938
OCLC Number: 1084316158
Notes: Introduction.-System Identification.-Classification.-Hybrid System Identification.- Exact Methods for Hybrid System Identification.-Estimation of Switched Linear/Affine Models.-Estimation of Piecewise Affine Models.-Recursive and State-space Identificationof Hybrid Systems.- Nonlinear Hybrid System Identification.
Description: 1 online resource (253 pages)
Contents: Intro; Preface; Contents; Notations; General Notations; Specific Notations; Abbreviations; List of Figures; List of Tables; 1 Introduction; 1.1 What are Hybrid Systems?; 1.1.1 Dynamical Systems; 1.1.2 Hybrid Systems; 1.2 What is System Identification?; 1.3 Applications; 1.4 Outline of the Book; References; 2 System Identification; 2.1 Input-Output (I/O) Models; 2.1.1 Models, Predictor, and Prediction Error; 2.1.2 Parameter Estimation; 2.1.3 Optimization; 2.2 State-Space (SS) Models; 2.2.1 Models and Properties; 2.2.2 Parameter Estimation; 2.3 Recursive Identification 2.4 Nonlinear System Identification ()2.4.1 Parametric Models; 2.4.2 Nonparametric Models; 2.5 Model Selection and Assessment; 2.5.1 Model Assessment; 2.5.2 Model Selection; References; 3 Classification; 3.1 Discrimination; 3.1.1 Binary Linear Classification; 3.1.2 Multi-class Problems; 3.1.3 Nonlinear Classification (); 3.2 Clustering; References; 4 Hybrid System Identification; 4.1 Hybrid System Models; 4.1.1 State-Space Versus Input-Output Models; 4.1.2 Linear Versus Nonlinear Submodels; 4.1.3 Piecewise Smooth Versus Arbitrarily Switched Systems; 4.2 Identification Problems 4.2.1 Hybrid System Identification with Unknown Mode4.2.2 The Trade-Off Between the Number of Modes and the Error; 4.2.3 Fixing the Number of Submodels; 4.2.4 Fixing a Bound on the Error; 4.2.5 Hybrid Model Assessment; 4.3 Other Related Problems (); 4.3.1 Nonlinear System Identification; 4.3.2 Subspace Clustering; References; 5 Exact Methods for Hybrid System Identification; 5.1 Straightforward Solutions; 5.1.1 Switching Regression with Fixed s; 5.1.2 Bounded-Error Estimation; 5.1.3 Piecewise Affine Regression with Fixed s; 5.2 Hardness Results (); 5.2.1 Basics in Computational Complexity 5.2.2 Hardness of Switching Regression5.2.3 Hardness of PWA Regression; 5.2.4 Hardness of Bounded-Error Estimation; 5.3 Polynomial-Time Algorithms for Fixed Dimensions; 5.3.1 PWA Regression with Fixed s and d; 5.3.2 Switching Regression with Fixed s and d; 5.3.3 Bounded-Error Estimation with Fixed d; 5.4 Global Optimization with Branch-and-Bound; 5.4.1 Switching Regression; 5.4.2 Bounded-Error Estimation; 5.4.3 PWA Regression; 5.5 The Need for Approximation Schemes/Heuristics; References; 6 Estimation of Switched Linear Models; 6.1 Fixed Number of Modes; 6.1.1 Algebraic Method 6.1.2 Continuous Optimization Approach6.1.3 Block-Coordinate Descent Approach; 6.2 Free Number of Modes; 6.2.1 Bounded-Error Approach; 6.2.2 Block-Coordinate Descent Approach; 6.2.3 Error Sparsification Method; 6.2.4 Parameter Sparsification Method; References; 7 Estimation of Piecewise Affine Models; 7.1 From Switched Affine Models to PWA Models; 7.2 From Nonlinear Models to PWA Models; 7.2.1 Limitation of the Classical Regularization Schemes; 7.2.2 Local Regularization; 7.2.3 Learning Smooth Models of PWA Functions by Convex Optimization; 7.2.4 Recovering PWA Models
Series Title: Lecture notes in control and information sciences, 478.
Responsibility: Fabien Lauer, Gérard Bloch.

Abstract:

Hybrid System Identification helps readers to build mathematical models of dynamical systems switching between different operating modes, from their experimental observations. It provides an overview of the interaction between system identification, machine learning and pattern recognition fields in explaining and analysing hybrid system identification. It emphasises the optimization and computational complexity issues that lie at the core of the problems considered and sets them aside from standard system identification problems. The book presents practical methods that leverage this complexity, as well as a broad view of state-of-the-art machine learning methods. The authors illustrate the key technical points using examples and figures to help the reader understand the material. The book includes an in-depth discussion and computational analysis of hybrid system identification problems, moving from the basic questions of the definition of hybrid systems and system identification to methods of hybrid system identification and the estimation of switched linear/affine and piecewise affine models. The authors also give an overview of the various applications of hybrid systems, discuss the connections to other fields, and describe more advanced material on recursive, state-space and nonlinear hybrid system identification. Hybrid System Identification includes a detailed exposition of major methods, which allows researchers and practitioners to acquaint themselves rapidly with state-of-the-art tools. The book is also a sound basis for graduate and undergraduate students studying this area of control, as the presentation and form of the book provides the background and coverage necessary for a full understanding of hybrid system identification, whether the reader is initially familiar with system identification related to hybrid systems or not.

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