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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.
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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