Related papers: Stabilization of a Chain of Three Hyperbolic PDEs …

This paper presents a backstepping approach for the boundary control of first-order hyperbolic equations with spatially varying coefficients posed on domains of arbitrary dimension. The method is based on a change of variables induced by…

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…

The paper is concerned with the strict-feedback form of hyperbolic distributed-parameter systems. Such a system structure is well known to be the basis for the recursive backstepping control design for nonlinear ODEs and is also reflected…

This paper deals with the exponential stability of systems made of a hyperbolic PDE coupled with an ODE with different time scales, the dynamics of the PDE being much faster than that of the ODE. Such a difference of time scales is modeled…

We present a new Partial Integral Equation (PIE) representation of Partial Differential Equations (PDEs) in which it is possible to use convex optimization to perform stability analysis with little or no conservatism. The first result gives…

Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing…

We propose a time domain decomposition approach to optimal control of partial differential equations (PDEs) based on semigroup theoretic methods. We formulate the optimality system consisting of two coupled forward-backward PDEs, the state…

This paper deals with the problem of boundary stabilization of first-order n\times n inhomogeneous quasilinear hyperbolic systems. A backstepping method is developed. The main result supplements the previous works on how to design…

The present work proposes a well-balanced finite volume-type numerical method for the solution of non-conservative hyperbolic partial differential equations (PDEs) with source terms. The method is characterized, first, by the use of a…

This paper is devoted to the study of hyperbolic systems of linear partial differential equations perturbed by a Brownian motion. The existence and uniqueness of solutions are proved by an energy method. The specific features of this class…

This work studies the stabilization for a periodic parabolic system under perturbations in the system conductivity. A perturbed system does not have any periodic solution in general. However, we will prove that the perturbed system can…

The problem of stabilization of a system of coupled PDEs of the forth-order by means of boundary control is investigated. The considered setup arises from the classical Euler-Bernoulli beam model, and constitutes a generalization of…

This paper proposes a framework to assess the stability of an ordinary differential equation which is coupled to a 1D-partial differential equation (PDE). The stability theorem is based on a new result on Integral Quadratic Constraints…

This paper establishes the equivalence between systems described by a single first-order hyperbolic partial differential equation and systems described by integral delay equations. System-theoretic results are provided for both classes of…

The paper addresses the boundary control of a class of hyperbolic PDEs, based on an equivalent representation in terms of an integral-difference equation. The situation is considered where direct compensation of reflection terms induces a…

In this paper, we will investigate the moment exponential stabilization of highly nonlinear hybrid stochastic differential delay equations. A periodically intermittent controller based on discrete time state observations with asynchronous…

First-order systems of hyperbolic partial differential equations (PDEs) occur ubiquitously throughout computational physics, commonly used in simulations of fluid turbulence, shock waves, electromagnetic interactions, and even general…

This work presents a numerical analysis of computing transition states of semilinear elliptic partial differential equations (PDEs) via the index-1 saddle dynamics, or equivalently, the gentlest ascent dynamics. To establish clear…

Simulations of the dynamics generated by partial differential equations (PDEs) provide approximate, numerical solutions to initial value problems. Such simulations are ubiquitous in scientific computing, but the correctness of the results…

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…