A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Reachability of weakly nonlinear systems using Carleman linearization
[article]

2021
*
arXiv
*
pre-print

*Using*a global error bound for the

*Carleman*

*linearization*abstraction, we are able to describe the full set

*of*behaviors

*of*the

*system*for sets

*of*initial conditions and in dense time. ... The novelty

*of*the approach is that we employ a particular embedding (

*Carleman*

*linearization*) to leverage recent advances

*of*high-dimensional

*reachability*solvers for

*linear*ordinary differential equations ... In Section 4 we describe how to propagate sets

*using*

*Carleman*

*linearization*. In Section 5 we extend this approach to a

*reachability*algorithm for dissipative

*nonlinear*dynamical

*systems*. ...

##
###
Uniqueness results for Stokes equations and their consequences in linear and nonlinear control problems

1996
*
E S A I M: Control, Optimisation and Calculus of Variations
*

The method

doi:10.1051/cocv:1996109
fatcat:cz7b57bvrrf65fdfxrwav5f5d4
*of*proof combines a suitable*linearization**of*the*system*with a xed point argument. We then are led to study the approximate controllability*of**linear*Stokes*systems*with potentials. ... This is done by means*of**Carleman*estimates. (1:1) Universit e P aris 12-Val de Marne, U.F.R. ... In a third section,*using*these unique continuation properties, we will deduce the approximate controllability for*linear*Stokes*systems*and, in particular, the case*of*the*linearized*Navier-Stokes equations ...##
###
Boundary Null Controllability With Constrained Control for a Nonlinear Two Stroke System: Application to Boundary Sentinel and Identification of Parameters in a Nonlinear Population Dynamics Model

2019
*
Journal of Mathematics Research
*

We first prove a new controllability result for a

doi:10.5539/jmr.v11n4p51
fatcat:ftdlv5n3uze2vo45laibvj7n6q
*nonlinear*two stroke*system*. The key to solve this controllability problem is an adapted*Carleman*inequality. ... Next, the obtained result is*used*to build a boundary sentinel to identify unknown parameters in a*nonlinear*population dynamics model with incomplete data. ...*Using*a derivation*of*Leray-Schauder fixed point theorem and*Carleman*inequality for the adjoint*system*, Traoré, O. ...##
###
Null and approximate controllability for weakly blowing up semilinear heat equations

2000
*
Annales de l'Institut Henri Poincare. Analyse non linéar
*

We prove that the

doi:10.1016/s0294-1449(00)00117-7
fatcat:phr2i5nrencojnnzpygss5nvwm
*system*is null-controllable at any time provided a globally defined and bounded trajectory exists and the*nonlinear*term f (y) is such that |f (s)| grows slower than |s| log 3/2 (1+|s ... Results*of*the same kind are proved in the context*of*approximate controllability. ... Indeed, as usual, we first*linearize*the*system*and show its controllability analyzing how the control depends*of*the size*of*the potential*of*the*linearized*equation. ...##
###
Null controllability of a nonlinear population dynamics problem

2006
*
International Journal of Mathematics and Mathematical Sciences
*

*Using*a derivation

*of*Leray-Schauder fixed point theorem and

*Carleman*inequality for the adjoint

*system*, we show that for all given initial density, there exists an internal control acting on a small open ... set

*of*the domain and leading the population to extinction. ... In what follows,

*using*a

*Carleman*inequality for an adjoint

*system*we establish a null controllability result for the

*nonlinear*population dynamics models stated in (1.1) when the initial distribution ...

##
###
Behavior of the Regularized Sampling Inverse Scattering Method at Internal Resonance Frequencies

2002
*
Electromagnetic Waves
*

NL, as it is presented in [1], has the following advantages over OLS: original

doi:10.2528/pier02092502
fatcat:d2xx2q47qngnzewhh6lgs66iru
*nonlinear*inverse problem is reduced to a finite sequence*of**linear*ones; resulting*linear*problem is one-dimensional while ... Natural*linearization*(NL) was introduced in [1] as an alternative to output least-squares (OLS) approach to*nonlinear*parameter identification problems for partial differential equations. ...*of*interfaces*using*elastic waves at fixed frequency. ...##
###
The cost of approximate controllability of heat equation with dynamical boundary conditions
[article]

2020
*
arXiv
*
pre-print

Combining new developed

arXiv:2006.06711v1
fatcat:giafp6gpxnabjfgib2d7f7xt6i
*Carleman*estimates and some optimization techniques, we obtain explicit bounds*of*the minimal norm control. We consider the*linear*and the semilinear cases. ... In this paper we study the cost*of*approximate controllability for this equation. ... in L 2 and, by*using*the*linearity*and the continuity*of*solution operator, we get ( ϕ n , ϕ n Γ ) = Φ n ⇀ Ψ = (ψ, ψ Γ )*weakly*in L 2 (0, T ; L 2 ), where Ψ is the solution*of*the adjoint*system*(4) ...##
###
Data-driven model order reduction of quadratic-bilinear systems

2018
*
Numerical Linear Algebra with Applications
*

For certain types

doi:10.1002/nla.2200
fatcat:b2qri6ktxzaftbye6zuzdcqaxe
*of**nonlinear**systems*, one can always find an equivalent QB model without performing any approximation. ... We illustrate the practical applicability*of*the proposed method by means*of*several numerical experiments resulting from semi-discretized*nonlinear*partial differential equations. † Data-Driven*System*... a projection based moment matching MOR approach that*uses*the quadratic-*linear*representation*of**nonlinear**systems*. ...##
###
Internal control of the Schrödinger equation

2014
*
Mathematical Control and Related Fields
*

In this paper, we intend to present some already known results about the internal controllability

doi:10.3934/mcrf.2014.4.161
fatcat:q4yhumgbznembp7yummy5olpn4
*of*the*linear*and*nonlinear*Schrödinger equation. ... After presenting the basic properties*of*the equation, we give a self contained proof*of*the controllability in dimension 1*using*some propagation results. ... I also thank Ivonne Rivas and Matthieu Léautaud for*useful*comments about the preliminary versions*of*these notes. ...##
###
Internal control of the Schrödinger equation
[article]

2013
*
arXiv
*
pre-print

In this paper, we intend to present some already known results about the internal controllability

arXiv:1307.2220v1
fatcat:2mggkyjzcfg7jjyhsnqhmm2vfm
*of*the*linear*and*nonlinear*Schr\"odinger equation. ... After presenting the basic properties*of*the equation, we give a self contained proof*of*the controllability in dimension 1*using*some propagation results. ... I also thank Ivonne Rivas and Matthieu Léautaud for*useful*comments about the preliminary versions*of*these notes. ...##
###
Global Controllability and Stabilization for the Nonlinear Schrödinger Equation on Some Compact Manifolds of Dimension 3

2010
*
SIAM Journal on Mathematical Analysis
*

We prove global internal controllability in large time for the

doi:10.1137/090749086
fatcat:egvylrsotjaq5dro2dnd55jsxi
*nonlinear*Schrödinger equation on some compact manifolds*of*dimension 3. ... We*use*Bourgain spaces. ... We can then*use*this remark and the work*of*S. Jaffard [23] and V. Komornik [25] for the*linear*equation on T n to get some local*nonlinear*results . ...##
###
Insensitizing control for linear and semi-linear heat equations with partially unknown domain

2018
*
E S A I M: Control, Optimisation and Calculus of Variations
*

It rests upon a

doi:10.1051/cocv/2018035
fatcat:ftopjvha4jhqtovczfwm6egzge
*linearization*procedure together with the*use**of*an appropriate fixed point theorem. ... We consider a semi-*linear*heat equation with Dirichlet boundary conditions and globally Lipschitz*nonlinearity*, posed on a bounded domain*of*R N (N ∈ N * ), assumed to be an unknown perturbation*of*a reference ... To conclude, let*us*mention that other*linear*or*nonlinear*parabolic*systems*coming from fluid mechanics have also been intensively studied, see for instance [4, 5, 13, 14] or [6] . ...##
###
Approximate controllability by birth control for a nonlinear population dynamics model

2010
*
E S A I M: Control, Optimisation and Calculus of Variations
*

In our proof we

doi:10.1051/cocv/2010043
fatcat:qezscwndmvf7np7pzwbn2pk7ui
*use*a unique continuation property for the solution*of*the heat equation and the Kakutani-Fan-Glicksberg fixed point theorem. ... In this paper we analyse an approximate controllability result for a*nonlinear*population dynamics model. ... The unique continuation result*used*there, is derived from a new*Carleman*inequality. ...##
###
Boundary Stabilization of the Korteweg-De Vries Equation
[chapter]

1994
*
Control and Estimation of Distributed Parameter Systems: Nonlinear Phenomena
*

The study

doi:10.1007/978-3-0348-8530-0_21
fatcat:n4jupoxc5vbdnkqwtfuptqyice
*of*the control and stabilization*of*the KdV equation began with the work*of*Russell and Zhang in late 1980s. ... A list*of*open problems is also provided for further investigation. ... The*linear*result was then extended to the*nonlinear**system*to obtain Theorem 3.1 by*using*the contraction mapping principle. ...##
###
Control and stabilization of the Korteweg-de Vries equation: recent progresses

2009
*
Journal of Systems Science and Complexity
*

The study

doi:10.1007/s11424-009-9194-2
fatcat:ww5fnubjzffvxp3jdfbao6mruq
*of*the control and stabilization*of*the KdV equation began with the work*of*Russell and Zhang in late 1980s. ... A list*of*open problems is also provided for further investigation. ... The*linear*result was then extended to the*nonlinear**system*to obtain Theorem 3.1 by*using*the contraction mapping principle. ...
« Previous

*Showing results 1 — 15 out of 30 results*