8 papers
RKHS method for computing Koopman-based Lyapunov functions
François-Grégoire Bierwart, Alexandre Mauroy
The Koopman operator is a powerful approach to global stability analysis of nonlinear systems, which provides a systematic procedure for Lyapunov function design. In this framework…
On Koopman Resolvents and Frequency Response of Nonlinear Systems
Yoshihiko Susuki, Natsuki Katayama, Alexandre Mauroy +1
This paper proposes a novel formulation of frequency response for nonlinear systems in the Koopman operator framework. This framework is a promising direction for the analysis and…
Global Linearization of Parameterized Nonlinear Systems with Stable Equilibrium Point Using the Koopman Operator
Natsuki Katayama, Alexandre Mauroy, Yoshihiko Susuki
The Koopman operator framework enables global analysis of nonlinear systems through its inherent linearity. This study aims to clarify spectral properties of the Koopman operators…
Error bounds on analytic Koopman-based Lyapunov functions
François-Grégoire Bierwart, Alexandre Mauroy
The Koopman operator provides an infinite-dimensional linear description of nonlinear dynamical systems that can be leveraged in the context of stability analysis. In particular, L…
A numerical Koopman-based framework to estimate regions of attraction for general vector fields
François-Grégoire Bierwart, Alexandre Mauroy
In this paper, we develop a comprehensive framework to estimate regions of attraction of equilibria for dynamics associated with general vector fields. This framework combines Koop…
Identification of Nonlinear Acyclic Networks in Continuous Time from Nonzero Initial Conditions and Full Excitations
Ramachandran Anantharaman, Renato Vizuete, Julien M. Hendrickx +1
This paper addresses the identifiability and identification of nonlinear acyclic networks in continuous time when the dynamics are located on the edges and all the nodes are excite…
Koopman operator based identification of nonlinear networks
Ramachandran Anantharaman, Alexandre Mauroy
In this work, we develop a method to identify continuous-time nonlinear networked dynamics via the Koopman operator framework. The proposed technique consists of two steps: the fir…
Dynamic Mode Decomposition with Non-uniform Sampling
Ramachandran Anantharaman, Alexandre Mauroy
Dynamic Mode Decomposition (DMD) and its extensions (EDMD) have been at the forefront of data-based approaches to Koopman operators. Most (E)DMD algorithms assume that the entire s…