### Abstract

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.

Original language | English |
---|---|

Publisher | Springer |

Number of pages | 559 |

Volume | 484 |

Edition | 1 |

ISBN (Electronic) | 978-3-030-35713-9 |

ISBN (Print) | 978-3-030-35712-2 |

DOIs | |

Publication status | Accepted/In press - 2019 |

### Publication series

Name | Lecture Notes in Control and Information Sciences |
---|

### Fingerprint

### Cite this

*The Koopman Operator in Systems and Control: Theory, Numerics, and Applications*. (1 ed.) (Lecture Notes in Control and Information Sciences). Springer. https://doi.org/10.1007/978-3-030-35713-9

}

*The Koopman Operator in Systems and Control: Theory, Numerics, and Applications*. Lecture Notes in Control and Information Sciences, vol. 484, 1 edn, Springer. https://doi.org/10.1007/978-3-030-35713-9

**The Koopman Operator in Systems and Control : Theory, Numerics, and Applications.** / Mauroy, Alexandre; Mezić, Igor; Susuki, Yoshihiko.

Research output: Book/Report/Journal › Book

TY - BOOK

T1 - The Koopman Operator in Systems and Control

T2 - Theory, Numerics, and Applications

AU - Mauroy, Alexandre

AU - Mezić, Igor

AU - Susuki, Yoshihiko

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

U2 - 10.1007/978-3-030-35713-9

DO - 10.1007/978-3-030-35713-9

M3 - Book

SN - 978-3-030-35712-2

VL - 484

T3 - Lecture Notes in Control and Information Sciences

BT - The Koopman Operator in Systems and Control

PB - Springer

ER -