Related papers: Sidewise control of 1-d waves
We consider a controlled reaction-diffusion equation, motivated by a pest eradication problem. Our goal is to derive a simpler model, describing the controlled evolution of a contaminated set. In this direction, the first part of the paper…
An optimal control problem for the linear wave equation with control cost chosen as the BV semi-norm in time is analyzed. This formulation enhances piecewise constant optimal controls and penalizes the number of jumps. Existence of optimal…
Exact controllability is proven on a graph with cycle. The controls can be a mix of controls applied at the boundary and interior vertices. The method of proof first uses a dynamical argument to prove shape controllability and velocity…
We study cascade coupled systems, for which our prototypical example is a 1-d heat equation coupled with a 1-d wave equation. The heat component is controlled through one boundary and the information is transmitted through another one to…
In this paper, we study some controllability and observability problems for stochastic systems coupling fourth- and second-order parabolic equations. The main goal is to control both equations with only one controller localized on the drift…
In recent years, controllability problems for dispersive systems have been extensively studied. This work is dedicated to proving a new type of controllability for a dispersive fifth order equation that models water waves, what we will now…
In this paper, we investigate the two-point boundary value problems for linear wave equation defined on a circle and prove that the equation possesses the exact controllability. We also investigate the two-point boundary value problems for…
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…
S. Hansen and E. Zuazua [SIAM J. Cont. Optim., 1995] studied the problem of exact controllability of two strings connected by a point mass with constant physical coefficients. In this paper we study the same problem with variable physical…
We provide a necessary and sufficient condition for a rough control driving a differential equation to be reconstructable, to some order, from observing the resulting controlled evolution. Physical examples and applications in stochastic…
The wave equation on a bounded domain of $\R^{n}$ with non homogeneous boundary Dirichlet data or sources supported on a subset of the boundary is considered. We analyze the problem of observing the source out of boundary measurements done…
The paper deals with the controllability of a degenerate beam equation. In particular, we assume that the left end of the beam is fixed, while a suitable control $f$ acts on the right end of it. As a first step we prove the existence of a…
We prove the internal controllability of some systems of two coupled wave equations in one space dimension, with one control, under certain conditions on the coupling. To do this we apply the "fictitious control method" in two cases:…
Controlling wave transmission is crucial for various applications. In this work, we apply the concept of unitary control to manipulate multiport wave transmission. Unitary control aims to control the behaviors of a set of orthogonal waves…
Self-optimizing control is a strategy for selecting controlled variables, where the economic objective guides the selection and design of controlled variables, with the expectation that maintaining the controlled variables at constant…
In this paper, we continue the study of some controllability issues for the forward stochastic parabolic equation with dynamic boundary conditions. The main novelty in the present paper consists of considering only one control without extra…
In this paper we prove that the Ball-Marsden-Slemrod controllability obstruction also holds for nonlinear equations, with integrable bilinear controls. We first show an abstract result and then we apply it to nonlinear wave equations. The…
We present a method to control the two-dimensional shape of traveling wave solutions to reaction-diffusion systems, as e.g. interfaces and excitation pulses. Control signals that realize a pre-given wave shape are determined analytically…
The inverse problem for the Sturm- Liouville operator with complex periodic potential and positive discontinuous coefficients on the axis is studied. Main characteristics of the fundamental solutions are investigated, the spectrum of the…
Within this chapter, we discuss control in the coefficients of an obstacle problem. Utilizing tools from H-convergence, we show existence of optimal solutions. First order necessary optimality conditions are obtained after deriving…