208 citations · 437 across the 22 of their papers we have counts for
31 papers
Analytic Extended Dynamic Mode Decomposition
Alexandre Mauroy, Igor Mezic
We develop a novel EDMD-type algorithm that captures the spectrum of the Koopman operator defined on a reproducing kernel Hilbert space of analytic functions. This method, which we…
Approximation of the Koopman operator via Bernstein polynomials
Rishikesh Yadav, Alexandre Mauroy
The Koopman operator approach provides a powerful linear description of nonlinear dynamical systems in terms of the evolution of observables. While the operator is typically infini…
On systematic criteria for the global stability of nonlinear systems via the Koopman operator framework
Christian Mugisho Zagabe, Alexandre Mauroy
We present novel sufficient conditions for the global stability of equilibria in the case of nonlinear dynamics with analytic vector fields. These conditions provide stability crit…
Uniform global stability of switched nonlinear systems in the Koopman operator framework
Christian Mugisho Zagabe, Alexandre Mauroy
In this paper, we provide a novel solution to an open problem on the global uniform stability of switched nonlinear systems. Our results are based on the Koopman operator approach…
A Sampling Theorem for Exact Identification of Continuous-time Nonlinear Dynamical Systems
Zhexuan Zeng, Zuogong Yue, Alexandre Mauroy +2
Low sampling frequency challenges the exact identification of the continuous-time (CT) dynamical system from sampled data, even when its model is identifiable. The necessary and su…
Spectral identification of networks with generalized diffusive coupling
Marvyn Gulina, Alexandre Mauroy
Spectral network identification aims at inferring the eigenvalues of the Laplacian matrix of a network from measurement data. This allows to capture global information on the netwo…
Koopman operator framework for spectral analysis and identification of infinite-dimensional systems
Alexandre Mauroy
We consider Koopman operator theory in the context of nonlinear infinite-dimensional systems, where the operator is defined over a space of bounded continuous functionals. The prop…
Koopman Resolvent: A Laplace-Domain Analysis of Nonlinear Autonomous Dynamical Systems
Yoshihiko Susuki, Alexandre Mauroy, Igor Mezic
The motivation of our research is to establish a Laplace-domain theory that provides principles and methodology to analyze and synthesize systems with nonlinear dynamics. A semigro…
Two methods to approximate the Koopman operator with a reservoir computer
Marvyn Gulina, Alexandre Mauroy
The Koopman operator provides a powerful framework for data-driven analysis of dynamical systems. In the last few years, a wealth of numerical methods providing finite-dimensional…
Global computation of phase-amplitude reduction for limit-cycle dynamics
A. Mauroy, I. Mezic
Recent years have witnessed increasing interest to phase-amplitude reduction of limit-cycle dynamics. Adding an amplitude coordinate to the phase coordinate allows to take into acc…
An Approach to Sparse Continuous-time System Identification from Unevenly Sampled Data
Rui Teixeira Ribeiro, Alexandre Mauroy, Jorge Goncalves
In this work, we address the problem of identifying sparse continuous-time dynamical systems when the spacing between successive samples (the sampling period) is not constant over…
Spectral identification of networks with inputs
Alexandre Mauroy, Julien Hendrickx
We consider a network of interconnected dynamical systems. Spectral network identification consists in recovering the eigenvalues of the network Laplacian from the measurements of…
Koopman-based lifting techniques for nonlinear systems identification
Alexandre Mauroy, Jorge Goncalves
We develop a novel lifting technique for nonlinear system identification based on the framework of the Koopman operator. The key idea is to identify the linear (infinitedimensional…
An Optimal Control Formulation of Pulse-Based Control Using Koopman Operator
Aivar Sootla, Alexandre Mauroy, Damien Ernst
In many applications, and in systems/synthetic biology, in particular, it is desirable to compute control policies that force the trajectory of a bistable system from one equilibri…
Geometric Properties of Isostables and Basins of Attraction of Monotone Systems
Aivar Sootla, Alexandre Mauroy
In this paper, we study geometric properties of basins of attraction of monotone systems. Our results are based on a combination of monotone systems theory and spectral operator th…
Shaping Pulses to Control Bistable Monotone Systems Using Koopman Operator
Aivar Sootla, Alexandre Mauroy, Jorge Goncalves
In this paper, we further develop a recently proposed control method to switch a bistable system between its steady states using temporal pulses. The motivation for using pulses co…
Linear identification of nonlinear systems: A lifting technique based on the Koopman operator
Alexandre Mauroy, Jorge Goncalves
We exploit the key idea that nonlinear system identification is equivalent to linear identification of the socalled Koopman operator. Instead of considering nonlinear system identi…
Spectral identification of networks using sparse measurements
A. Mauroy, J. Hendrickx
We propose a new method to recover global information about a network of interconnected dynamical systems based on observations made at a small number (possibly one) of its nodes.…
The Four Bars Problem
Alexandre Mauroy, Perouz Taslakian, Stefan Langerman +1
A four-bar linkage is a mechanism consisting of four rigid bars which are joined by their endpoints in a polygonal chain and which can rotate freely at the joints (or vertices). We…
Differential positivity characterizes one-dimensional normally hyperbolic attractors
Fulvio Forni, Alexandre Mauroy, Rodolphe Sepulchre
The paper shows that normally hyperbolic one-dimensional compact attractors of smooth dynamical systems are characterized by differential positivity, that is, the pointwise infinit…
Properties of Isostables and Basins of Attraction of Monotone Systems
Aivar Sootla, Alexandre Mauroy
In this paper, we investigate geometric properties of monotone systems by studying their isostables and basins of attraction. Isostables are boundaries of specific forward-invarian…
Operator-Theoretic Characterization of Eventually Monotone Systems
Aivar Sootla, Alexandre Mauroy
Monotone systems are dynamical systems whose solutions preserve a partial order in the initial condition for all positive times. It stands to reason that some systems may preserve…
Properties of Eventually Positive Linear Input-Output Systems
Aivar Sootla
In this paper, we consider the systems with trajectories originating in the nonnegative orthant becoming nonnegative after some finite time transient. First we consider dynamical s…
A spectral characterization of nonlinear normal modes
Giuseppe Ilario Cirillo, Alexandre Mauroy, Ludovic Renson +2
This paper explores the relationship that exists between nonlinear normal modes (NNMs) defined as invariant manifolds in phase space and the spectral expansion of the Koopman opera…