Related papers: Variable Support Control for the Wave Equation: A …
This paper deals with a one-dimensional wave equation with a nonlinear dynamic boundary condition and a Neumann-type boundary control acting on the other extremity. We consider a class of nonlinear stabilizing feedbacks that only depend on…
In this paper, we study the observability and controllability of wave equations coupled by first or zero order terms on a compact manifold. We adopt the approach in Dehman-Lebeau's paper \cite{DehmanLebeau09} to prove that: the weak…
We consider optimal control of the scalar wave equation where the control enters as a coefficient in the principal part. Adding a total variation penalty allows showing existence of optimal controls, which requires continuity results for…
In this paper, motivated by the study of optimal control problems for infinite dimensional systems with endpoint state constraints, we introduce the notion of finite codimensional (exact/approximate) controllability. Some equivalent…
We design observer-based controllers to stabilise abstract linear boundary control systems on Hilbert spaces. Our main results introduce conditions for exponential, strong, and polynomial stability, and establish external well-posedness of…
This analysis is concerned with the controllability of quantum systems in the case where the standard dipolar approximation, involving the permanent dipole moment of the system, is corrected with a polarizability term, involving the field…
A widely used stochastic wave equation is the classical wave equation perturbed by a term of It\^o's integral. We show that this equation is not exactly controllable even if the controls are effective everywhere in both the drift and the…
This paper establishes the local exact controllability of the quasilinear porous media equation with Dirichlet boundary condition.\\ Consider the equation $$\begin{aligned} &y_t - \Delta a(y) = mu+f \text{ on } Q\\ &y(0)=y_0,\ y…
We study the exact controllability for spatially periodic water waves with surface tension, by localized exterior pressures applied to free surfaces. We prove that in any dimension, the exact controllability holds within arbitrarily short…
In this paper we introduce some new concepts for second-order hyperbolic equations: two-point boundary value problem, global exact controllability and exact controllability. For several kinds of important linear and nonlinear wave equations…
We propose a spectral collocation method to approximate the exact boundary control of the wave equation in a square domain. The idea is to introduce a suitable approximate control problem that we solve in the finite-dimensional space of…
In this paper, we study the exact controllability and stabilization of a system of two wave equations coupled by velocities with an internal, local control acting on only one equation. We distinguish two cases. In the first one, when the…
We consider the operator $H:= \partial_t -\Delta+V$ in 2D or 3D waveguide. With an adapted global Carleman estimate with singular weight functions we give a stability result for the time dependent part of the potential for this particular…
This review surveys previous and recent results on null controllability and inverse problems for parabolic systems with dynamic boundary conditions. We aim to demonstrate how classical methods such as Carleman estimates can be extended to…
We discuss several new results on nonnegative approximate controllability for the one-dimensional Heat equation governed by either multiplicative or nonnegative additive control, acting within a proper subset of the space domain at every…
The question of what conditions should be set at the nodes of a discrete graph for the wave equation with discrete time is investigated. The variational method for the derivation of these conditions is used. A parallel with the continuous…
We will consider exact controllability of the distributed system governed by the wave equation with memory. It will be proved that this mechanical system can be driven to rest in finite time, the absolute value of the distributed control…
This work is devoted to prove the pointwise controllability of the Bernoulli-Euler beam equation. It is obtained as a limit of internal controllability of the same type of equation.
This paper is addressed to studying the exact controllability for stochastic Schr\"{o}dinger equations by two controls. One is a boundary control in the drift term and the other is an internal control in the diffusion term. By means of the…
In this paper we study the exact controllability problem for the wave equation on a finite metric graph with the Kirchhoff-Neumann matching conditions. Among all vertices and edges we choose certain active vertices and edges, and give a…