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The Koopman Operator in Systems and Control Concepts, Methodologies, and Applications
Title
The Koopman Operator in Systems and Control [electronic resource] : Concepts, Methodologies, and Applications / edited by Alexandre Mauroy, Igor Mezić, Yoshihiko Susuki.
ISBN
9783030357139
Edition
1st ed. 2020.
Publication
Cham : Springer International Publishing : Imprint: Springer, 2020.
Physical Description
1 online resource (XXIII, 556 p.) 138 illus., 85 illus. in color.
Local Notes
Access is available to the Yale community.
Access and use
Access restricted by licensing agreement.
Summary
This book provides a broad overview of state-of-the-art research at the intersection of the Koopman operator theory and control theory. It also reviews novel theoretical results obtained and efficient numerical methods developed within the framework of Koopman operator theory. The contributions discuss the latest findings and techniques in several areas of control theory, including model predictive control, optimal control, observer design, systems identification and structural analysis of controlled systems, addressing both theoretical and numerical aspects and presenting open research directions, as well as detailed numerical schemes and data-driven methods. Each contribution addresses a specific problem. After a brief introduction of the Koopman operator framework, including basic notions and definitions, the book explores numerical methods, such as the dynamic mode decomposition (DMD) algorithm and Arnoldi-based methods, which are used to represent the operator in a finite-dimensional basis and to compute its spectral properties from data. The main body of the book is divided into three parts: theoretical results and numerical techniques for observer design, synthesis analysis, stability analysis, parameter estimation, and identification; data-driven techniques based on DMD, which extract the spectral properties of the Koopman operator from data for the structural analysis of controlled systems; and Koopman operator techniques with specific applications in systems and control, which range from heat transfer analysis to robot control. A useful reference resource on the Koopman operator theory for control theorists and practitioners, the book is also of interest to graduate students, researchers, and engineers looking for an introduction to a novel and comprehensive approach to systems and control, from pure theory to data-driven methods.
Variant and related titles
Springer ENIN.
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Format
Books / Online
Language
English
Added to Catalog
February 26, 2020
Series
Lecture Notes in Control and Information Sciences, 484
Contents
Part I: Control Design, Observation, and Identification
Linear Observer Synthesis for Nonlinear Systems
Linear Predictors for Nonlinear Dynamical Systems
Global Stability Analysis
Pulse-based Optimal Control
Parameter Estimation and Identification of Nonlinear Systems
Koopman Spectrum and Stability of Cascaded Dynamical Systems
Open and Closed Loop Control of PDEs via Switched Systems and Koopman operator based reduced order models
Part II: Data-Driven Analysis
Data-driven Approximations of Dynamical Systems Operators for Control
Operator Theoretic-based Data-driven Approach for Optimal Stabilization of Nonlinear System
Manifold Learning for Data-Driven Dynamical Systems Analysis
Use of Data-Driven Koopman Spectrum Computation and Delay Embedding
Part III: Applications
Modeling of Advective Heat Transfer in a Practical Building Atrium via Koopman Mode Decomposition
Phase-amplitude Reduction of Limit-cycling Systems
Exploiting Effects of Network Topology on Performance in Nonlinear Consensus Networks
Koopman Operators in Embedded Control.
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