Sorin Micu

Uniform boundary controllability of a semi-discrete 1-D wave equation

Summary. A numerical scheme for the controlled semi-discrete 1-D wave equation is considered. We analyze the convergence of the boundary controls of the semi-discrete equations to a control of the continuous wave equation when the mesh size tends to zero. We prove that, if the high modes of the discrete initial data have been filtered out, there exists a sequence of uniformly bounded controls and any weak limit of this sequence is a control for the continuous problem. The number of the eliminated frequencies depends on the mesh size and the regularity of the continuous initial data. The case of the HUM controls is also discussed.

On the lack of null-controllability of the heat equation on the half-line

We consider the linear heat equation on the half-line with a Dirichlet boundary control. We analyze the null-controllability problem. More precisely, we study the class of initial data that may be driven to zero in finite time by means of an appropriate choice of the L2 boundary control. We rewrite the system on the similarity variables that are a common tool when analyzing asymptotic problems. Next, the control problem is reduced to a moment problem which turns out to be critical since it concerns the family of real exponentials {eit }j> in which the usual summability condition on the inverses of the eigenvalues does not hold. Roughly speaking, we prove that controllable data have Fourier coefficients that grow exponentially for large frequencies. This result is in contrast with the existing ones for bounded domains that guarantee that every initial datum belonging to a Sobolev space of negative order may be driven to zero in an arbitrarily small time.

On the Controllability of the Linearized Benjamin--Bona--Mahony Equation

We study the boundary controllability properties of the linearized Benjamin--Bona--Mahony equation

An Approximation Method for Exact Controls of Vibrating Systems

\left\{ \begin{array}{ll} u_t-u_{xxt}+u_x=0,& x\in(0,1),\,t>0,\\ u(t,0)=0,\,\, u(1,t)=f(t),&t>0. \end{array} \right. We show that the equation is approximately controllable but not spectrally controllable (no finite linear combination of eigenfunctions, other than zero, is controllable). Next, we prove a finite controllability result and we estimate the norms of the controls needed in this case.

Asymptotics for the spectrum of a fluid/struture hybrid system arising in the control of noise

The null-controllability property of a

Uniform Boundary Controllability of a Semidiscrete 1-D Wave Equation with Vanishing Viscosity

1-d

On a Weakly Damped System Arising in the Control of Noise

parabolic equation involving a fractional power of the Laplace operator,

Approximation of the controls for the linear beam equation

(-\Delta)^\alpha

Analysis of a Hybrid System for Noise Reduction

, is studied. The control is a scalar time-dependent function