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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…
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…
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…
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…
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…
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…
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).…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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.…
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…
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…
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)…