Related papers: Kernel-based Koopman approximants for control: Fle…
Recently Koopman operator has become a promising data-driven tool to facilitate real-time control for unknown nonlinear systems. It maps nonlinear systems into equivalent linear systems in embedding space, ready for real-time linear control…
Koopman analysis provides a general framework from which to analyze a nonlinear dynamical system in terms of a linear operator acting on an infinite-dimensional observable space. This theoretical framework provides a rigorous underpinning…
A novel dynamic mode decomposition (DMD) method based on a Kalman filter is proposed. This paper explains the fast algorithm of the proposed Kalman filter DMD (KFDMD) in combination with truncated proper orthogonal decomposition for…
The Koopman operator theory is an increasingly popular formalism of dynamical systems theory which enables analysis and prediction of the nonlinear dynamics from measurement data. Building on the recent development of the Koopman model…
This paper introduces a new theoretical and computational framework for a data driven Koopman mode analysis of nonlinear dynamics. To alleviate the potential problem of ill-conditioned eigenvectors in the existing implementations of the…
Koopman decomposition is a non-linear generalization of eigen-decomposition, and is being increasingly utilized in the analysis of spatio-temporal dynamics. Well-known techniques such as the dynamic mode decomposition (DMD) and its linear…
Koopman operators and transfer operators represent nonlinear dynamics in state space through its induced action on linear spaces of observables and measures, respectively. This framework enables the use of linear operator theory for…
Koopman operators are infinite-dimensional operators that globally linearize nonlinear dynamical systems, making their spectral information valuable for understanding dynamics. However, Koopman operators can have continuous spectra and…
Approximating the Koopman operator from data is numerically challenging when many lifting functions are considered. Even low-dimensional systems can yield unstable or ill-conditioned results in a high-dimensional lifted space. In this…
Koopman operators are infinite-dimensional operators that linearize nonlinear dynamical systems, facilitating the study of their spectral properties and enabling the prediction of the time evolution of observable quantities. Recent methods…
An efficient way to control systems with unknown nonlinear dynamics is to find an appropriate embedding or representation for simplified approximation (e.g. linearization), which facilitates system identification and control synthesis.…
We propose an analytical construction of observable functions in the extended dynamic mode decomposition (EDMD) algorithm. EDMD is a numerical method for approximating the spectral properties of the Koopman operator. The choice of…
This paper presents a generalizable methodology for data-driven identification of nonlinear dynamics that bounds the model error in terms of the prediction horizon and the magnitude of the derivatives of the system states. Using…
This paper proposes a robust nonlinear observer synthesis method for a population of systems modelled using the Koopman operator. The Koopman operator allows nonlinear systems to be rewritten as infinite-dimensional linear systems. A…
Learning models of dynamical systems characterized by specific stability properties is of crucial importance in applications. Existing results mainly focus on linear systems or some limited classes of nonlinear systems and stability…
Koopman operators linearize nonlinear dynamical systems, making their spectral information of crucial interest. Numerous algorithms have been developed to approximate these spectral properties, and Dynamic Mode Decomposition (DMD) stands…
Koopman operators globally linearize nonlinear dynamical systems and their spectral information is a powerful tool for the analysis and decomposition of nonlinear dynamical systems. However, Koopman operators are infinite-dimensional, and…
We present a method to design a state-feedback controller ensuring exponential stability for nonlinear systems using only measurement data. Our approach relies on Koopman-operator theory and uses robust control to explicitly account for…
In this paper we prove new connections between two frameworks for analysis and control of nonlinear systems: the Koopman operator framework and contraction analysis. Each method, in different ways, provides exact and global analyses of…
Providing efficient and accurate parametrizations for model reduction is a key goal in many areas of science and technology. Here we present a strong link between data-driven and theoretical approaches to achieving this goal. Formal…