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Publications associées (12)

Koopman-based Data-driven Robust Control of Nonlinear Systems Using Integral Quadratic Constraints

Alireza Karimi, Mert Eyuboglu

This paper introduces a novel method for data-driven robust control of nonlinear systems based on the Koopman operator, utilizing Integral Quadratic Constraints (IQCs). The Koopman operator theory facilitates the linear representation of nonlinear system d ...

2024

Data-Driven Control Synthesis using Koopman Operator: A Robust Approach

Alireza Karimi, Nathan Russell Powell, Mert Eyuboglu

This paper proposes a data-driven control design method for nonlinear systems that builds upon the Koopman operator framework. In particular, the Koopman operator is used to lift the nonlinear dynamics to a higher-dimensional space where the so-called obse ...

2024

Learning Physics-Consistent Particle Interactions

Olga Fink, David Simon Kammer

Interacting particle systems play a key role in science and engineering. Access to the governing particle interaction law is fundamental for a complete understanding of such systems. However, the inherent system complexity keeps the particle interaction hi ...

Oxford University Press2023

Koopmans Spectral Functionals in Periodic Boundary Conditions

Nicola Marzari, Nicola Colonna, Edward Baxter Linscott, Riccardo De Gennaro

Koopmans spectral functionals aim to describe simultaneously ground-state properties and charged excitations of atoms, molecules, nanostructures, and periodic crystals. This is achieved by augmenting standard density functionals with simple but physically ...

AMER CHEMICAL SOC2022

Spectral properties of extended systems from Koopmans-compliant functionals

Riccardo De Gennaro

Electronic-structure simulations have been impacting the study of materials properties thanks to the simplicity of density-functional theory, a method that gives access to the ground state of the system. Although very important, ground-state properties rep ...

EPFL2022

Bloch's theorem in orbital-density-dependent functionals: Band structures from Koopmans spectral functionals

Nicola Marzari, Nicola Colonna, Edward Baxter Linscott, Riccardo De Gennaro

Koopmans-compliant functionals provide an orbital-density-dependent framework for an accurate evaluation of spectral properties; they are obtained by imposing a generalized piecewise-linearity condition on the total energy of the system with respect to the ...

AMER PHYSICAL SOC2022

On Gaussian Process Based Koopman Operators

Colin Neil Jones

Enabling analysis of non-linear systems in linear form, the Koopman operator has been shown to be a powerful tool for system identification and controller design. However, current data-driven methods cannot provide quantification of model uncertainty given ...

ELSEVIER2020

Feedback Control Design Maximizing the Region of Attraction of Stochastic Systems Using Polynomial Chaos Expansion

Petr Listov

A feedback control design is proposed for stochastic systems with finite second moment which aims at maximising the region of attraction of the equilibrium point. Polynomial Chaos (PC) expansions are employed to represent the stochastic closed loop system ...

ELSEVIER2020

Learning Feature Maps of the Koopman Operator: A Subspace Viewpoint

Colin Neil Jones, Yingzhao Lian

The Koopman operator was recently shown to be a useful method for nonlinear system identification and controller design. However, the scalability of current data-driven approaches is limited by the selection of feature maps. In this paper, we present a new ...

IEEE2019

Cantor systems, piecewise translations and simple amenable groups

Nicolas Monod

We provide the first examples of finitely generated simple groups that are amenable (and infinite). This follows from a general existence result on invariant states for piecewise-translations of the integers. The states are obtained by constructing a suita ...

Annal Mathematics2013

Coded Modulation Based on Higher Dimensional Chaotic Maps

Thomas Schimming, Slobodan Kozic

In this paper we examine coded modulations based on iterations of higher dimensional piece-wise linear maps(PWLM). Particulary, we study a generalization of the Bernoulli map in higher dimensions and its application to communications. In the proposed schem ...

2005

Finite element approximation of multi-scale elliptic problems using patches of elements

Jacques Rappaz

In this paper we present a method for the numerical solution of elliptic problems with multi-scale data using multiple levels of not necessarily nested grids. The method consists in calculating successive corrections to the solution in patches whose discre ...

Springer2005