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The Koopman operator in systems and ...

Mauroy, Alexandre.

The Koopman operator in systems and controlconcepts, methodologies, and applications /

Record Type:	Electronic resources : Monograph/item
Title/Author:	The Koopman operator in systems and controledited by Alexandre Mauroy, Igor Mezic, Yoshihiko Susuki.
Reminder of title:	concepts, methodologies, and applications /
other author:	Mauroy, Alexandre.
Published:	Cham :Springer International Publishing :2020.
Description:	xxiii, 556 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Operator theory.
Online resource:	https://doi.org/10.1007/978-3-030-35713-9
ISBN:	9783030357139$q(electronic bk.)

The Koopman operator in systems and controlconcepts, methodologies, and applications /
The Koopman operator in systems and controlconcepts, methodologies, and applications /[electronic resource] :edited by Alexandre Mauroy, Igor Mezic, Yoshihiko Susuki. - Cham :Springer International Publishing :2020. - xxiii, 556 p. :ill. (some col.), digital ;24 cm. - Lecture notes in control and information sciences,v.4840170-8643 ;. - Lecture notes in control and information sciences ;315..

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.

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.

ISBN: 9783030357139$q(electronic bk.)

Standard No.: 10.1007/978-3-030-35713-9doiSubjects--Topical Terms:

229156
Operator theory.

LC Class. No.: QA329 / .K667 2020

Dewey Class. No.: 515.724

The Koopman operator in systems and controlconcepts, methodologies, and applications /
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505 0 $a 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.
520 $a 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.
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