Related papers: Regulating the $P^+ = 0$ Singularity
The global approach to control systems which we have been pursuing in other work favours the study of dynamics achievable through control. It employs certain globally defined geometric objects and attempts to describe them in the general…
The main methods for controlling the biphoton field, as well as the problems for which the width and the shape of the spectrum of the biphoton field are of decisive importance, are discussed. The method for controlling the spectrum of the…
As the size of an optical vortex knot, imprinted in a coherent light beam, is decreased, nonparaxial effects alter the structure of the knotted optical singularity. For knot structures approaching the scale of wavelength, longitudinal…
We study the controllability of the multidimensional wave equation in a bounded domain with Dirichlet boundary condition, in which the support of the control is allowed to change over time. The exact controllability is reduced to the proof…
The paper deals with exact null-controllability problem for a linear control system consisting of two serially connected abstract control systems. Controllability conditions are obtained. Applications to the exact null-controllability for…
We derive in a straightforward way the exact controllability of the 1-D Schrodinger equation with a Dirichlet boundary control. We use the so-called flatness approach, which consists in parameterizing the solution and the control by the…
The most basic scenario of quantum control involves the organized manipulation of pure dynamical states of the system by means of unitary transformations. Recently, Vilela Mendes and Mank'o have shown that the conditions for controllability…
Approximate controllability of the Euler equations is investigated by means of a finite set of actuators. It is proven that approximate controllability holds if we can find a saturating subset of actuators. The notion of saturating set is…
Here we describe a simple and fundamental approach to the maximal L^p regularity of parabolic equations, which only uses the concept of singular integrals of Volterra type. Knowledge of analytic semigroups, R-boundedness or…
This paper reviews the design of regulation loops for power converters. Power converter control being a vast domain, it does not aim to be exhaustive. The objective is to give a rapid overview of the main synthesis methods in both…
The aim of this paper is analyzing existence, multiplicity, and regularity issues for the positive solutions of a Neumann boundary value problem of superlinear indefinite type related to the mean curvature operator with a sublinear…
We give sharp regularity conditions, ensuring the backward uniquess property to a class of parabolic operators.
This paper is devoted to the study of the null and approximate controllability for some classes of linear coupled parabolic systems with less controls than equations. More precisely, for a given bounded domain in R^N, we consider a system…
We study here a singular perturbation problem of biLaplacian type, which can be seen as the biharmonic counterpart of classical combustion models. We provide different results, that include the convergence to a free boundary problem driven…
This article develops variational integrators for a class of underactuated mechanical systems using the theory of discrete mechanics. Further, a discrete optimal control problem is formulated for the considered class of systems and…
A new systematic approach to the construction of approximate solutions to a class of nonlinear singularly perturbed feedback control systems using the boundary layer functions especially with regard to the possible occurrence of the…
This paper investigates a novel mechanism for quasi-singularity formation in both linear and nonlinear hyperbolic wave equations in two and three dimensions. We prove that over any finite time interval, there exist inputs such that the…
In this paper we try to settle some confused points concerning the use of the notion of p-nuclearity in the mathematical and physical literature, pointing out that the nuclearity index in the physicists' sense vanishes for any p > 1. Our…
Manipulating radiation asymmetry of photonic structures is of particular interest in many photonic applications such as directional optical antenna, high efficiency on-chip lasers, and coherent light control. Here, we proposed a term of…
A general class of singular abstract Cauchy problems is considered which naturally arises in applications to certain Free Boundary Problems. Existence of an associated evolution operator characterizing its solutions is established and is…