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In this paper, we present a rapid boundary stabilization of a Timoshenko beam with anti-damping and anti-stiffness at the uncontrolled boundary, by using PDE backstepping. We introduce a transformation to map the Timoshenko beam states into…

Optimization and Control · Mathematics 2022-07-12 Guangwei Chen , Rafael Vazquez , Miroslav Krstic

We consider an inverse problem involving the reconstruction of the solution to a nonlinear partial differential equation (PDE) with unknown boundary conditions. Instead of direct boundary data, we are provided with a large dataset of…

Numerical Analysis · Mathematics 2025-07-30 Erik Burman , Mats G. Larson , Karl Larsson , Carl Lundholm

This work is devoted to the stabilization of parabolic systems with a finite-dimensional control subjected to a constant delay. Our main result shows that the Fattorini-Hautus criterion yields the existence of such a feedback control, as in…

Optimization and Control · Mathematics 2020-04-20 Imene Aicha Djebour , Takéo Takahashi , Julie Valein

This paper considers the backstepping state feedback and observer design for hyperbolic and parabolic PDEs, which are bidirectionally interconnected in a general coupling structure. Both PDE subsystems consist of coupled scalar PDEs with…

Systems and Control · Electrical Eng. & Systems 2023-06-23 Joachim Deutscher , Nicole Gehring , Nick Jung

This paper focuses on switching event-triggered output feedback control for a class of parabolic partial differential equation (PDE) systems subject to unknown nonlinearities and external bounded disturbance. Initially, the PDE systems is…

Optimization and Control · Mathematics 2024-12-30 Xiao-Yu Sun , Chuan Zhang , Huai-Ning Wu , Xian-Fu Zhang

We develop a control design for stabilization of traffic flow in congested regime, based on an Aw-Rascle-Zhang-type (ARZ-type) Partial Differential Equation (PDE) model, for traffic consisting of both ACC-equipped (Adaptive Cruise…

Optimization and Control · Mathematics 2018-12-20 Nikolaos Bekiaris-Liberis , Argiris I. Delis

The stability of stationary solutions of first-order systems of PDE's are considered. They may include some singular geometric terms, leading to discontinuous flux and non-conservative products. Based on several examples in Fluid Mechanics,…

Analysis of PDEs · Mathematics 2017-09-15 Nicolas Seguin

In this work stability results for systems described by coupled Retarded Functional Differential Equations (RFDEs) and Functional Difference Equations (FDEs) are presented. The results are based on the observation that the composite system…

Dynamical Systems · Mathematics 2007-05-23 Iasson Karafyllis , Pierdomenico Pepe , Zhong-Ping Jiang

Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or…

Computational Physics · Physics 2016-03-02 Fabian Spill , Pilar Guerrero , Tomas Alarcon , Philip K. Maini , Helen Byrne

A novel approach to design the feedback control based on past states is proposed for hybrid stochastic differential equations (HSDEs). This new theorem builds up the connection between the delay feedback control and the control function…

Optimization and Control · Mathematics 2019-07-30 Junhao Hu , Wei Liu , Feiqi Deng , Xuerong Mao

This paper presents the analysis of the stability properties of PID controllers for dynamical systems with multiple state delays, focusing on the mathematical characterization of the potential sensitivity of stability with respect to…

Optimization and Control · Mathematics 2020-09-08 Pieter Appeltans , Silviu-Iulian Niculescu , Wim Michiels

For population systems modeled by age-structured hyperbolic partial differential equations (PDEs), we redesign the existing feedback laws, designed under the assumption that the dilution input is directly actuated, to the more realistic…

Optimization and Control · Mathematics 2023-06-27 Paul-Erik Haacker , Iasson Karafyllis , Miroslav Krstić , Mamadou Diagne

Control of systems where the information between the controller, actuator, and sensor can be lost or delayed can be challenging with respect to stability and performance. One way to overcome the resulting problems is the use of prediction…

Optimization and Control · Mathematics 2011-09-27 Rolf Findeisen , Lars Grüne , Jürgen Pannek , Paolo Varutti

This paper addresses the problem of input-to-state stabilization for a class of parabolic equations with time-varying coefficients, as well as Dirichlet and Robin boundary disturbances. By using time-invariant kernel functions, which can…

Optimization and Control · Mathematics 2024-06-18 Yongchun Bi , Jun Zheng , Guchuan Zhu

The objective of this paper is to report some computational results for the theory of DAE stability boundary, with the aim of advancing applications in power system voltage stability studies. Firstly, a new regularization transformation for…

Systems and Control · Electrical Eng. & Systems 2025-08-06 Zhenyao Li , Yifan Yao , Deqiang Gan

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

Retarded stochastic differential equations (SDEs) constitute a large collection of systems arising in various real-life applications. Most of the existing results make crucial use of dissipative conditions. Dealing with "pure delay" systems…

Probability · Mathematics 2013-08-12 Jianhai Bao , George Yin , Chenggui Yuan

In this paper, we introduce the notion of relative $\mathcal{K}$-equi-stability (RKES) to characterize the uniformly continuous dependence of (weak) solutions on external disturbances for nonlinear parabolic PDE systems. Based on the RKES,…

Optimization and Control · Mathematics 2021-02-03 Jun Zheng , Guchuan Zhu , Sergey Dashkovskiy

In this paper, we consider the stability analysis of large-scale distributed networked control systems with random communication delays between linearly interconnected subsystems. The stability analysis is performed in the Markov jump…

Systems and Control · Computer Science 2015-11-13 Kooktae Lee , Raktim Bhattacharya

We perform various numerical tests to study the effect of (boundary) stenosis on blood flow stability, employing a detailed and accurate, second-order finite-volume scheme for numerically implementing a partial differential equation (PDE)…

Numerical Analysis · Mathematics 2024-08-05 Shantanu Singh , Nikolaos Bekiaris-Liberis