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This paper presents the control and stabilization of the rotary inverted pendulum based on a general controller scheme. The proposed scheme has its foundation in classical control theory, and the importance of an integrator in disturbance…

Systems and Control · Electrical Eng. & Systems 2022-09-07 Justin Jacob , Navin Khaneja

We study the robust output regulation of linear boundary control systems by constructing extended systems. The extended systems are established based on solving static differential equations under two new conditions. We first consider the…

Optimization and Control · Mathematics 2021-04-19 Duy Phan , Lassi Paunonen

This paper studies the robustness of a PDE backstepping delay-compensated boundary controller for a reaction-diffusion partial differential equation (PDE) with respect to a nominal delay subject to stochastic error disturbance. The…

Optimization and Control · Mathematics 2024-01-22 Dandan Guan , Jie Qi , Mamadou Diagne

In this paper, we study the indirect stabilization problem for a system of two coupled semilinear wave equations with internal damping in a bounded domain in $\mathbb{R}^3$. The nonlinearity is assumed to be subcritical, defocusing and…

Analysis of PDEs · Mathematics 2024-07-08 Radhia Ayechi , Moez Khenissi , Camille Laurent

This article is concerned with the energy decay of an infinite memory wave equation with a logarithmic nonlinear term and a frictional damping term. The problem is formulated in a bounded domain in $\mathbb R^d$ ($d\ge3$) with a smooth…

Analysis of PDEs · Mathematics 2025-12-03 Qingqing Peng , Yikan Liu

The paper investigates dynamical systems for which the derivative of some positive-definite function along the solutions of this system depends on so-called density function. In turn, such dynamical systems are called density systems. The…

Systems and Control · Electrical Eng. & Systems 2025-01-30 Igor Furtat

This paper is concerned with the regulation control of a one-dimensional reaction-diffusion equation in the presence of a state-delay in the reaction term. The objective is to achieve the PI regulation of the right Dirichlet trace with a…

Optimization and Control · Mathematics 2021-08-25 Hugo Lhachemi , Ammar Malik , Robert Shorten

We report experimental results on the decay of wave turbulence in an elastic plate obtained by stopping the forcing from a stationary turbulent state. In the stationary case, the forcing is seen to induce some anisotropy and a spectrum in…

Chaotic Dynamics · Physics 2015-05-28 Benjamin Miquel , Nicolas Mordant

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

We present an alternative "encapsulated" formulation of the Selective Frequency Damping method for finding unstable equilibria of dynamical systems, which is particularly useful when analysing the stability of fluid flows. The formulation…

Fluid Dynamics · Physics 2015-06-18 Bastien E. Jordi , C. J. Cotter , Spencer J. Sherwin

We consider a degenerate/singular wave equation in one dimension, with drift and in presence of a leading operator which is not in divergence form. We impose a homogeneous Dirichlet boundary condition where the degeneracy occurs and a…

Analysis of PDEs · Mathematics 2024-03-27 Genni Fragnelli , Dimitri Mugnai , Amine Sbai

We outline a method for controlling the location of stable and unstable manifolds in the following sense. From a known location of the stable and unstable manifolds in a steady two-dimensional flow, the primary segments of the manifolds are…

Dynamical Systems · Mathematics 2016-01-07 Sanjeeva Balasuriya , Kathrin Padberg-Gehle

We consider the inverse dynamic problem for the wave equation with a potential on an interval $(0,2\pi)$ with periodic boundary conditions. We use a boundary triplet to set up the initial-boundary value problem. As an inverse data we use a…

Analysis of PDEs · Mathematics 2025-05-27 A. S. Mikhaylov , V. S. Mikhaylov

Classical discrete-time adaptive controllers provide asymptotic stabilization. While the original adaptive controllers did not handle noise or unmodelled dynamics well, redesigned versions were proven to have some tolerance; however,…

Optimization and Control · Mathematics 2017-11-28 Daniel E. Miller

In this article we prove semiglobal stabilization and exact controllability results for nonlinear plate equations with hinged boundary conditions and analytic nonlinearity. These results hold when the damping or control is localized in a…

Analysis of PDEs · Mathematics 2025-11-24 Cristóbal Loyola

This paper addresses the stabilization of a chain of three coupled hyperbolic partial differential equations actuated by two control inputs applied at arbitrary nodes of the network. With the exception of configurations where one input is…

Optimization and Control · Mathematics 2026-04-24 Adam Braun , Jean Auriol , Lucas Brivadis

This paper studies the polynomial stabilization of an elastic plate with dynamical boundary conditions on a non-smooth domain. To deal with the possible loss of solution regularity induced by boundary singularities, we formulate the problem…

Analysis of PDEs · Mathematics 2026-04-08 Ya-nan Sun , Qiong Zhang

In this paper, we investigate the rapid stabilizability of linear infinite-dimensional control systems with constant delays. Under the assumptions that the state operator generates an immediately compact semigroup and that the delay…

Optimization and Control · Mathematics 2026-04-21 Yaxing Ma , Lijuan Wang , Huaiqiang Yu

In this paper, we concentrate on the exponential stabilization of stochastic nonlinear systems. Different from the single event-triggering mechanism in traditional deterministic/stochastic control systems, based on two stopping time…

Dynamical Systems · Mathematics 2023-06-01 Xuetao Yang , Quanxin Zhu

This study considers the stability of a non-inflectional elastica under a conservative end force subject to the Dirichlet, mixed, and Neumann boundary conditions. It is demonstrated that the non-inflectional elastica subject to the…

Classical Physics · Physics 2018-12-20 Milan Batista