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We present a pseudo-reversible normalizing flow method for efficiently generating samples of the state of a stochastic differential equation (SDE) with different initial distributions. The primary objective is to construct an accurate and…

Numerical Analysis · Mathematics 2023-06-12 Minglei Yang , Pengjun Wang , Diego del-Castillo-Negrete , Yanzhao Cao , Guannan Zhang

This paper presents an output feedback control law for the Korteweg-de Vries equation. The control design is based on the backstepping method and the introduction of an appropriate observer. The local exponential stability of the…

Analysis of PDEs · Mathematics 2016-09-28 Swann Marx , Eduardo Cerpa

In this paper, we present output feedback boundary stabilization for a class of semilinear parabolic PDEs with a boundary measurement and an actuation located at the same place. The method uses backstepping transformations, where the state…

Analysis of PDEs · Mathematics 2016-12-13 Agus Hasan

Stabilization of a coupled system consisting of a parabolic partial differential equation and an elliptic partial differential equation is considered. Even in the situation when the parabolic equation is exponentially stable on its own, the…

Optimization and Control · Mathematics 2023-09-04 Ala' Alalabi , Kirsten Morris

A backstepping-based compensator design is developed for a system of $2\times2$ first-order linear hyperbolic partial differential equations (PDE) in the presence of an uncertain long input delay at boundary. We introduce a transport PDE to…

Optimization and Control · Mathematics 2023-07-24 Jing Zhang , Jie Qi

We propose a novel Skew Gradient Embedding (SGE) framework for systematically reformulating thermodynamically consistent partial differential equation (PDE) models-capturing both reversible and irreversible processes-as generalized gradient…

Numerical Analysis · Mathematics 2025-09-24 Xuelong Gu , Qi Wang

We propose a new design technique for the stabilization of coupled ODE-PDE systems in feedforward form. In particular, we address the stabilization problem of a one-dimensional transport equation driven by a scalar ODE which is controlled…

Systems and Control · Electrical Eng. & Systems 2020-10-27 Swann Marx , Lucas Brivadis , Daniele Astolfi

In this article we study the so-called water tank system. In this system, the behavior of water contained in a 1-D tank is modelled by Saint-Venant equations, with a scalar distributed control. It is well-known that the linearized systems…

Analysis of PDEs · Mathematics 2022-05-11 Jean-Michel Coron , Amaury Hayat , Shengquan Xiang , Christophe Zhang

We develop backstepping state feedback control to stabilize a moving shockwave in a freeway segment under bilateral boundary actuations of traffic flow. A moving shockwave, consisting of light traffic upstream of the shockwave and heavy…

Optimization and Control · Mathematics 2019-04-10 Huan Yu , Mamadou Diagne , Liguo Zhang , Miroslav Krstic

A magnetizable piezoelectric beam model, free at both ends, is considered. Piezoelectric materials have a strong interaction of electromagnetic and acoustic waves, whose wave propagation speeds differ substantially. The corresponding…

Analysis of PDEs · Mathematics 2024-03-14 Ahmet Ozkan Ozer , Uthman Rasaq , Ibrahim Khalilullah

We propose, analyze, and investigate numerically a novel feedback control strategy for high Reynolds number flows. For both the continuous and the discrete (finite element) settings, we prove that the new strategy yields accurate results…

Numerical Analysis · Mathematics 2025-07-11 Maria Strazzullo , Francesco Ballarin , Traian Iliescu , Claudio Canuto

In this work, we consider the problem of boundary stabilization for a quasilinear 2X2 system of first-order hyperbolic PDEs. We design a new full-state feedback control law, with actuation on only one end of the domain, which achieves H^2…

Optimization and Control · Mathematics 2012-09-03 Jean-Michel Coron , Rafael Vazquez , Miroslav Krstic , Georges Bastin

We introduce a control design and analysis framework for micro-macro, boundary control of large-scale, $n+m$ hyperbolic PDE systems. Specifically, we develop feedback laws for stabilization of hyperbolic systems at the micro level (i.e., of…

Optimization and Control · Mathematics 2025-10-15 Jukka-Pekka Humaloja , Nikolaos Bekiaris-Liberis

The dynamic partial differential equation (PDE) model governing longitudinal oscillations in magnetizable piezoelectric beams exhibits exponentially stable solutions when subjected to two boundary state feedback controllers. An analytically…

Optimization and Control · Mathematics 2024-10-10 Ahmet Ozkan Ozer , Ahmet Kaan Aydin , Rafi Emran

In this paper, a backstepping observer and an output feedback control law are designed for the stabilization of the one-phase Stefan problem. The present result is an improvement of the recent full state feedback backstepping controller…

Optimization and Control · Mathematics 2016-09-28 Shumon Koga , Mamadou Diagne , Miroslav Krstic

The present paper develops boundary output-feedback stabilization of the Korteweg-de Vries (KdV) equation with sensors and an actuator located at different boundaries (anti collocated set-up) using backstepping method. The feedback control…

Analysis of PDEs · Mathematics 2016-03-30 Agus Hasan

We develop a backstepping control design for a class of continuum systems of linear hyperbolic PDEs, described by a coupled system of an ensemble of rightward transporting PDEs and a (finite) system of $m$ leftward transporting PDEs. The…

Optimization and Control · Mathematics 2024-10-30 Jukka-Pekka Humaloja , Nikolaos Bekiaris-Liberis

This paper deals with the backstepping design of observer-based compensators for parabolic ODE-PDE-ODE systems. The latter consist of n coupled parabolic PDEs with distinct diffusion coefficients and spatially-varying coefficients, that are…

Systems and Control · Electrical Eng. & Systems 2020-08-28 Joachim Deutscher , Nicole Gehring

In this paper, we design an output-feedback controller to stabilize n +m hetero-directional transport partial differential equations (PDEs) coupled on both domain boundaries to ordinary differential equations (ODEs). This class of systems…

Analysis of PDEs · Mathematics 2024-06-17 Jean Auriol , Federico Bribiesca Argomedo

In this paper, we design a controller for an interconnected system composed of a linear Stochastic Differential Equation (SDE) controlled through a linear hetero-directional hyperbolic Partial Differential Equation (PDE). Our objective is…

Optimization and Control · Mathematics 2025-02-19 Gabriel Velho , Jean Auriol , Islam Boussaada , Riccardo Bonalli