Publications related to Finite-time stabilization in optimal time of homogeneous quasilinear hyperbolic systems in one dimensional space

Related publications (39)

Initial Conditions Impact on Nonlinear Dynamics of a Loudspeaker

In contrast with linear systems, forced oscillations at particular frequencies may result in more than one stable limit cycle in the dynamic response of a nonlinear system. Also known as jump phenomenon, in these frequency regions, a nonlinear system would ...

European Acoustics Association2024

Stable cones in the thin one-phase problem

Xavier Fernandez-Real Girona

The aim of this work is to study homogeneous stable solutions to the thin (or fractional) one -phase free boundary problem. The problem of classifying stable (or minimal) homogeneous solutions in dimensions n >= 3 is completely open. In this context, axial ...

Johns Hopkins Univ Press2024

Critical degeneracy in a nonlinear hyperbolic equation can produce atypical instability

Charles Stuart

This paper deals with the initial value problem for a semilinear wave equation on a bounded domain and solutions are required to vanish on the boundary of this domain. The essential feature of the situation considered here is that the ellipticity of the sp ...

2024

Navigating the Loop: From Control Systems to Neural Networks and Back

Clara Lucía Galimberti

The work presented in this thesis lies at the intersection of Machine Learning (ML) and control theory. The first part is dedicated to the design of Deep Neural Network (DNN) architectures with specific numerical properties, inspired by dynamical systems m ...

EPFL2024

Ultrabroadband sound control of 3D spaces using plasmacoustic metalayers

Hervé Lissek, Stanislav Sergeev

Controlling sound in three-dimensional spaces is a complex task, challenged by the intricacies of acoustic modal structures, the variety of noise sources, and the propagation of waves. This research analyzes the influence of local impedance control on the ...

Institute of Noise Control Engineering2024

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

Positional Embeddings for Solving PDEs with Evolutional Deep Neural Networks

Jan Sickmann Hesthaven, Mariella Kast

This work extends the paradigm of evolutional deep neural networks (EDNNs) to solving parametric time -dependent partial differential equations (PDEs) on domains with geometric structure. By introducing positional embeddings based on eigenfunctions of the ...

2024

Stochastic pairwise preference convergence in Bayesian agents

Max-Olivier Hongler

Beliefs inform the behaviour of forward-thinking agents in complex environments. Recently, sequential Bayesian inference has emerged as a mechanism to study belief formation among agents adapting to dynamical conditions. However, we lack critical theory to ...

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

Global existence for perturbations of the 2D stochastic Navier-Stokes equations with space-time white noise

Martin Hairer

We prove global in time well-posedness for perturbations of the 2D stochastic Navier-Stokes equations partial derivative( t)u + u center dot del u = Delta u - del p + sigma + xi, u(0, center dot ) = u(0),div (u) = 0, driven by additive space-time white noi ...

Springernature2024

Experimental observation of topological transition in linear and nonlinear parametric oscillators

Romain Christophe Rémy Fleury, Benjamin Apffel

Parametric oscillators are examples of externally driven systems that can exhibit two stable states with opposite phase depending on the initial conditions. In this work, we propose to study what happens when the external forcing is perturbed by a continuo ...

2024

Reactive collision-free motion generation in joint space via dynamical systems and sampling-based MPC

Aude Billard, Nadia Barbara Figueroa Fernandez, Mikhail Koptev

Dynamical system (DS) based motion planning offers collision-free motion, with closed-loop reactivity thanks to their analytical expression. It ensures that obstacles are not penetrated by reshaping a nominal DS through matrix modulation, which is construc ...

Sage Publications Ltd2024

A graph convolutional autoencoder approach to model order reduction for parametrized PDEs

Jan Sickmann Hesthaven, Federico Pichi

The present work proposes a framework for nonlinear model order reduction based on a Graph Convolutional Autoencoder (GCA-ROM). In the reduced order modeling (ROM) context, one is interested in obtaining real -time and many-query evaluations of parametric ...

Academic Press Inc Elsevier Science2024

Koopman analysis of the periodic Korteweg-de Vries equation

Jeremy Peter Parker

The eigenspectrum of the Koopman operator enables the decomposition of nonlinear dynamics into a sum of nonlinear functions of the state space with purely exponential and sinusoidal time dependence. For a limited number of dynamical systems, it is possible ...

American Institute of Physics2023

Nonlinear dynamics and Kerr frequency comb formation in lattices of coupled microresonators

Tobias Kippenberg, Alexey Tikan, Aleksandr Tusnin

Recently, substantial progress has been made in the understanding of microresonators frequency combs based on dissipative Kerr solitons (DKSs). However, most of the studies have focused on the single-resonator level. Coupled resonator systems can open new ...

Nature Portfolio2023

One-Dimensional "Ghost Imaging" in Electron Microscopy of Inelastically Scattered Electrons

Fabrizio Carbone, Ivan Madan, Giovanni Maria Vanacore, Simone Gargiulo

Entanglement and correlation are at the basis of quantummechanicsand have been used in optics to create a framework for "ghostimaging". We propose that a similar scheme can be used in anelectron microscope to exploit the correlation of electrons with theco ...

2023

Infrared-active phonons in one-dimensional materials and their spectroscopic signatures

Nicola Marzari, Thibault Daniel Pierre Sohier, Norma Rivano

Dimensionality provides a clear fingerprint on the dispersion of infrared-active, polar-optical phonons. For these phonons, the local dipoles parametrized by the Born effective charges drive the LO-TO splitting of bulk materials; this splitting actually br ...

Nature Portfolio2023

Emergent non-Hermitian localization phenomena in the synthetic space of zero-dimensional bosonic systems

Fabrizio Minganti

Phase transitions in non-Hermitian systems are at the focus of cutting edge theoretical and experimental research. On the one hand, parity-time- (PT-) and anti-PT-symmetric physics have gained ever-growing interest, due to the existence of non-Hermitian sp ...

AMER PHYSICAL SOC2023

Localization errors of the stochastic heat equation

David Jean-Michel Candil

In this thesis, we study the stochastic heat equation (SHE) on bounded domains and on the whole Euclidean space

\R^d.

We confirm the intuition that as the bounded domain increases to the whole space, both solutions become arbitrarily close to one another ...

EPFL2022

Stabilized isogeometric discretizations on trimmed and union geometries, and weak imposition of the boundary conditions for the Darcy flow

Riccardo Puppi

Modern manufacturing engineering is based on a ``design-through-analysis'' workflow. According to this paradigm, a prototype is first designed with Computer-aided-design (CAD) software and then finalized by simulating its physical behavior, which usually i ...

EPFL2022