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

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

Control systems operating in real-world environments often face disturbances arising from measurement noise and model mismatch. These factors can significantly impact the perfor- mance and safety of the system. In this thesis, we aim to leverage data to de ...

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

Chat with Graph Search

Stable cones in the thin one-phase problem

Critical degeneracy in a nonlinear hyperbolic equation can produce atypical instability

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

Ultrabroadband sound control of 3D spaces using plasmacoustic metalayers

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

Positional Embeddings for Solving PDEs with Evolutional Deep Neural Networks

Stochastic pairwise preference convergence in Bayesian agents

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

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

Experimental observation of topological transition in linear and nonlinear parametric oscillators

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

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

Koopman analysis of the periodic Korteweg-de Vries equation

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

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

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

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

Localization errors of the stochastic heat equation

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

Data-Driven Control and Optimization under Noisy and Uncertain Conditions