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In this paper, we establish the existence of a positive, bounded solution for a class of parabolic partial differential equations with nonlinear boundary conditions, where the boundary conditions depend on the solution on the boundary at a…

Dynamical Systems · Mathematics 2025-07-15 Gangadhara Boregowda , Michael R. Lindstrom

This paper discusses the in-domain feedback stabilization of reaction-diffusion PDEs with Robin boundary conditions in the presence of an uncertain time- and spatially-varying delay in the distributed actuation. The proposed control design…

Optimization and Control · Mathematics 2021-08-18 Hugo Lhachemi , Christophe Prieur , Robert Shorten

In this paper, we study the stability of solutions of stochastic McKean-Vlasov equations (SMVEs) via feedback control based on discrete-time state observation. By using a specific Lyapunov function, the $H_{\infty}$ stability, asymptotic…

Probability · Mathematics 2021-10-25 Hao Wu , Junhao Hu , Shuaibin Gao , Chenggui Yuan

We propose a Bayesian framework for feedback boundary control for hyperbolic balance laws. The method propagates a probability distribution over feedback parameters by using Lyapunov decay estimates as a likelihood. In the linear setting,…

Numerical Analysis · Mathematics 2026-02-03 Markus Bambach , Shaoshuai Chu , Michael Herty , Yunong Lin

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…

Probability · Mathematics 2021-09-29 Adnan Aboulalaa

We consider an elliptic PDE in two variables. As one parameter approaches zero, this PDE collapses to a parabolic one, that is forward parabolic in a part of the domain and backward parabolic in the remainder. Such problems arise naturally…

Analysis of PDEs · Mathematics 2007-05-23 Diego Dominici , Charles Knessl

We study the long-term qualitative behavior of randomly perturbed dynamical systems. More specifically, we look at limit cycles of stochastic differential equations (SDE) with Markovian switching, in which the process switches at random…

Probability · Mathematics 2024-07-10 Nguyen H. Du , Alexandru Hening , Dang H. Nguyen , George Yin

We use the backstepping method to study the stabilization of a 1-D linear transport equation on the interval (0, L), by controlling the scalar amplitude of a piecewise regular function of the space variable in the source term. We prove that…

Optimization and Control · Mathematics 2019-11-21 Christophe Zhang

The focus of this work is on local stability of a class of nonlinear ordinary differential equations (ODE) that describe limits of empirical measures associated with finite-state weakly interacting N-particle systems. Local Lyapunov…

Probability · Mathematics 2015-02-16 Amarjit Budhiraja , Paul Dupuis , Markus Fischer , Kavita Ramanan

We present an optimization-based framework for analysis and control of linear parabolic partial differential equations (PDEs) with spatially varying coefficients without discretization or numerical approximation. For controller synthesis,…

Systems and Control · Computer Science 2016-09-06 Aditya Gahlawat , Matthew M. Peet

This paper explores a fully discrete approximation for a nonlinear hyperbolic PDE-constrained optimization problem (P) with applications in acoustic full waveform inversion. The optimization problem is primarily complicated by the…

Numerical Analysis · Mathematics 2025-01-22 Luis Ammann , Irwin Yousept

We extend the convergence analysis for methods solving PDE-constrained optimal control problems containing both discrete and continuous control decisions based on relaxation and rounding strategies to the class of first order semilinear…

Optimization and Control · Mathematics 2015-09-15 Falk M. Hante

In this paper, we study the stabilization problem of quantum spin-1/2 systems under continuous-time measurements. In the case without feedback, we show exponential stabilization around the excited and ground state by providing a lower bound…

Quantum Physics · Physics 2019-02-12 Weichao Liang , Nina H. Amini , Paolo Mason

This paper investigates the robustness of exponential stability of a class of switched systems described by linear functional differential equations under arbitrary switching. We will measure the stability robustness of such a system,…

Dynamical Systems · Mathematics 2022-03-08 Nguyen Khoa Son , Le Van Ngoc

This paper presents a maximum principle-based approach in the establishment of input-to-state stability (ISS) for a class of nonlinear parabolic partial differential equations (PDEs) over higher dimensional domains with variable…

Analysis of PDEs · Mathematics 2020-05-25 Jun Zheng , Guchuan Zhu

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

This paper considers the robust cooperative output regulation for a network of parabolic PDE systems. The solution of this problem is obtained by extending the cooperative internal model principle from finite to infinite dimensions. For a…

Optimization and Control · Mathematics 2020-10-22 Joachim Deutscher

This work is devoted to the almost sure stabilization of adaptive control systems that involve an unknown Markov chain. The control system displays continuous dynamics represented by differential equations and discrete events given by a…

Probability · Mathematics 2008-07-10 Bernard Bercu , Francois Dufour , G. George Yin

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

Linear Parameter-Varying (LPV) systems with jumps and piecewise differentiable parameters is a class of hybrid LPV systems for which no tailored stability analysis and stabilization conditions have been obtained so far. We fill this gap…

Optimization and Control · Mathematics 2020-12-07 Corentin Briat