16,464 research outputs found
The Coron System
Coron is a domain and platform independent, multi-purposed data mining
toolkit, which incorporates not only a rich collection of data mining
algorithms, but also allows a number of auxiliary operations. To the best of
our knowledge, a data mining toolkit designed specifically for itemset
extraction and association rule generation like Coron does not exist elsewhere.
Coron also provides support for preparing and filtering data, and for
interpreting the extracted units of knowledge
Control Lyapunov Functions and Stabilization by Means of Continuous Time-Varying Feedback
For a general time-varying system, we prove that existence of an "Output
Robust Control Lyapunov Function" implies existence of continuous time-varying
feedback stabilizer, which guarantees output asymptotic stability with respect
to the resulting closed-loop system. The main results of the present work
constitute generalizations of a well-known result towards feedback
stabilization due to J. M. Coron and L. Rosier concerning stabilization of
autonomous systems by means of time-varying periodic feedback.Comment: Submitted for possible publication to ESAIM Control, Optimisation and
Calculus of Variation
Local controllability of 1D Schr\"odinger equations with bilinear control and minimal time
We consider a linear Schr\"odinger equation, on a bounded interval, with
bilinear control.
Beauchard and Laurent proved that, under an appropriate non degeneracy
assumption, this system is controllable, locally around the ground state, in
arbitrary time. Coron proved that a positive minimal time is required for this
controllability, on a particular degenerate example.
In this article, we propose a general context for the local controllability
to hold in large time, but not in small time. The existence of a positive
minimal time is closely related to the behaviour of the second order term, in
the power series expansion of the solution
Explicit approximate controllability of the Schr\"odinger equation with a polarizability term
We consider a controlled Schr\"odinger equation with a dipolar and a
polarizability term, used when the dipolar approximation is not valid. The
control is the amplitude of the external electric field, it acts non linearly
on the state. We extend in this infinite dimensional framework previous
techniques used by Coron, Grigoriu, Lefter and Turinici for stabilization in
finite dimension. We consider a highly oscillating control and prove the
semi-global weak stabilization of the averaged system using a Lyapunov
function introduced by Nersesyan. Then it is proved that the solutions of the
Schr\"odinger equation and of the averaged equation stay close on every finite
time horizon provided that the control is oscillating enough. Combining these
two results, we get approximate controllability to the ground state for the
polarizability system
Dissipative boundary conditions for 2 × 2 hyperbolic systems of conservation laws for entropy solutions in BV
International audienceIn this article, we investigate the BV stability of 2×2 hyperbolic systems of conservation laws with strictly positive velocities under dissipative boundary conditions. More precisely, we derive sufficient conditions guaranteeing the exponential stability of the system under consideration for entropy solutions in BV. Our proof is based on a front tracking algorithm used to construct approximate piecewise constants solutions whose BV norms are controlled through a Lyapunov functional. This Lyapunov functional is inspired by the one proposed in J. Glimm's seminal work [J. Glimm, Comm. Pure Appl. Math., 18:697--715, 1965], modified with some suitable weights in the spirit of the previous works [J.-M. Coron, G. Bastin, and B. d'Andréa Novel, SIAM J. Control Optim., 47(3):1460--1498, 2008] and [J.-M. Coron, B. d'Andréa Novel, and G. Bastin, IEEE Trans. Automat. Control, 52(1):2--11, 2007]
Remarks on global controllability for the shallow-water system with two control forces
In this paper we deal with the compressible Navier-Stokes equations with a
friction term in one dimension on an interval. We study the exact
controllability properties of this equation with general initial condition when
the boundary control is acting at both endpoints of the interval. Inspired by
the work of Guerrero and Imanuvilov in \cite{GI} on the viscous Burger
equation, we prove by choosing irrotational data and using the notion of
effective velocity developed in \cite{cpde,cras} that the exact global
controllability result does not hold for any time
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