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We introduce a finite dimensional version of backstepping controller design for stabilizing solutions of PDEs from boundary. Our controller uses only a finite number of Fourier modes of the state of solution, as opposed to the classical…

Optimization and Control · Mathematics 2024-12-30 Varga Kalantarov , Türker Özsarı , Kemal Cem Yılmaz

This paper addresses boundary prescribed-time stabilization of a one-dimensional heat equation with spatially and temporally varying coefficients. In contrast to asymptotic or exponential stabilization, prescribed-time stabilization ensures…

Optimization and Control · Mathematics 2026-02-27 Kaijing Lyu , Umberto Biccari , Jun-Min Wang

We consider a one-dimensional controlled reaction-diffusion equation, where the control acts on the boundary and is subject to a constant delay. Such a model is a paradigm for more general parabolic systems coupled with a transport…

Optimization and Control · Mathematics 2015-11-11 Delphine Bresch-Pietri , Christophe Prieur , Emmanuel Trélat

We consider $\hinf$-optimal state-feedback control of the class of linear Partial Differential Equations (PDEs) which admit a Partial Integral Equation (PIE) representation. While linear matrix inequalities are commonly used for optimal…

Optimization and Control · Mathematics 2026-04-07 Sachin Shivakumar , Amritam Das , Matthew Peet

Research on stabilization of coupled hyperbolic PDEs has been dominated by the focus on pairs of counter-convecting ("heterodirectional") transport PDEs with distributed local coupling and with controls at one or both boundaries. A recent…

Optimization and Control · Mathematics 2015-04-29 Long Hu , Florent Di Meglio , Rafael Vazquez , Miroslav Krstic

We propose a physics-informed consistency modeling framework for solving partial differential equations (PDEs) via fast, few-step generative inference. We identify a key stability challenge in physics-constrained consistency training, where…

Machine Learning · Computer Science 2026-02-11 Che-Chia Chang , Chen-Yang Dai , Te-Sheng Lin , Ming-Chih Lai , Chieh-Hsin Lai

We present a convolutional framework which significantly reduces the complexity and thus, the computational effort for distributed reinforcement learning control of dynamical systems governed by partial differential equations (PDEs).…

Machine Learning · Computer Science 2023-12-27 Sebastian Peitz , Jan Stenner , Vikas Chidananda , Oliver Wallscheid , Steven L. Brunton , Kunihiko Taira

Recently, the problem of boundary stabilization for unstable linear constant-coefficient coupled reaction-diffusion systems was solved by means of the backstepping method. The extension of this result to systems with advection terms and…

Optimization and Control · Mathematics 2016-03-17 Rafael Vazquez , Miroslav Krstic

A general system of n ordinary differential equations coupled with one reaction-diffusion equation, considered in a bounded N-dimensional domain, with no-flux boundary condition is studied in a context of pattern formation. Such initial…

Analysis of PDEs · Mathematics 2023-04-14 Szymon Cygan , Grzegorz Karch , Anna Marciniak-Czochra , Kanako Suzuki

In this paper, we design a controller for an interconnected system consisting of a linear Stochastic Differential Equation (SDE) actuated through a linear hyperbolic Partial Differential Equation (PDE). Our approach aims to minimize the…

Optimization and Control · Mathematics 2024-05-15 Gabriel Velho , Jean Auriol , Riccardo Bonalli , Islam Boussaada

This paper focuses on the input-to-state stabilization problem for an ordinary differential equation (ODE) cascaded by parabolic partial differential equation (PDE) in the presence of Dirichlet-Robin boundary disturbances, as well as…

Optimization and Control · Mathematics 2026-02-11 Yongchun Bi , Jun Zheng , Guchuan Zhu

We consider an interlinked production model consisting of conservation laws (PDE) coupled to ordinary differential equations (ODE). Our focus is the analysis of control laws for the coupled system and corresponding stabilization questions…

Optimization and Control · Mathematics 2019-12-13 Vanessa Baumgärtner , Simone Göttlich , Stephan Knapp

In this paper, we consider the exponential stabilization and observation of an unstable heat equation in a general multi-dimensional domain by combining the finite-dimensional spectral truncation technique and the recently developed…

Systems and Control · Electrical Eng. & Systems 2021-02-05 Hongyinping Feng , Pei-Hua Lang , Jiankang Liu

This paper is concerned with the distributed control and stabilization problems for linear discrete-time large scale systems with imposed constraints. The main contributions of this paper are: Firstly, by using the maximum principle…

Optimization and Control · Mathematics 2018-01-03 Qingyuan Qi , Huanshui Zhang , Peijun Ju

Diffusion models have recently emerged as powerful stochastic frameworks for high-dimensional inference and generation. However, existing applications to partial differential equations (PDEs) predominantly rely on physics-informed training…

Numerical Analysis · Mathematics 2026-04-03 Yi Bing , Liu Jia , Fu Jinyang , Peng Xiang

We study the boundary stabilization of one-dimensional cross-diffusion systems in a moving domain. We show first exponential stabilization and then finite-time stabilization in arbitrary small-time of the linearized system around uniform…

Analysis of PDEs · Mathematics 2023-07-14 Jean Cauvin-Vila , Virginie Ehrlacher , Amaury Hayat

In this paper, we solve the problem of exponential stabilization for a class of cascade ODE-PDE system governed by a linear ordinary differential equation and a 1-d linearized Korteweg-de Vries equation (KdV) posed on a bounded interval.…

Analysis of PDEs · Mathematics 2018-01-04 Habib Ayadi

We develop a novel multi-layer predictor-feedback to achieve exact compensation of state-dependent input delay of general nonlinear integro-differential equations. The system of interest is an unconventional mixed Partial Differential…

Optimization and Control · Mathematics 2026-04-09 Tong Li , Peipei Shang , Mamadou Diagne

In this paper we study the stability of explicit finite difference discretizations of linear advection-diffusion equations (ADE) with arbitrary order of accuracy in the context of method of lines. The analysis first focuses on the stability…

Numerical Analysis · Mathematics 2020-06-17 Xianyi Zeng , Md Mahmudul Hasan

We study the problem of distributed control of large-scale robotic swarms which can be modeled as continuum densities evolving under the continuity equation. We propose a formalization of distributed controllers as (generally nonlinear)…

Systems and Control · Electrical Eng. & Systems 2026-05-01 Max Emerick , Saroj Prasad Chhatoi , Bassam Bamieh