ISSN 2156-8472(print)
ISSN 2156-8499(online) |
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MCRF aims to publish original research as well as expository papers on mathematical control theory and related fields. The goal is to provide a complete and reliable source of mathematical methods and results in this field. The journal will also accept papers from some related fields such as differential equations, functional analysis, probability theory and stochastic analysis, inverse problems, optimization, numerical computation, mathematical finance, information theory, game theory, system theory, etc., provided that they have some intrinsic connections with control theory.
MCRF is a quarterly publication in March, June, September and December. The journal will be online only. It is edited by a group of international leading experts in mathematical control theory and related fields. A key feature of MCRF is the journal's rapid publication, with a special emphasis on the highest scientific standard. The journal is essential reading for scientists and researchers who wish to keep abreast of the latest developments in the field. MCRF is a publication of the American Institute of Mathematical Sciences. All rights reserved. |
TOP 10 Most Read Articles in MCRF, May 2012
| 1 |
Numerical methods for dividend optimization using
regime-switching jump-diffusion models
Volume 1, Number 1, Pages: 21 - 40, 2011
Zhuo Jin,
George Yin
and Hailiang Yang
 Abstract
 References
 Full Text
Related Articles
This work develops numerical methods for finding optimal dividend
policies to maximize the expected present value of dividend
payout, where the surplus follows a regime-switching jump
diffusion model and the switching is represented by a
continuous-time Markov chain. To approximate the optimal dividend
policies or optimal controls, we use Markov chain approximation
techniques to construct a discrete-time controlled Markov chain
with two components. Under simple conditions, we prove the
convergence of the approximation sequence to the surplus process
and the convergence of the approximation to the value function.
Several examples are provided to demonstrate the performance of
the algorithms.
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| 2 |
A deterministic linear quadratic time-inconsistent
optimal control problem
Volume 1, Number 1, Pages: 83 - 118, 2011
Jiongmin Yong
Abstract
References
Full Text
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A time-inconsistent optimal control problem is formulated and
studied for a controlled linear ordinary differential equation with
a quadratic cost functional. A notion of time-consistent equilibrium
strategy is introduced for the original time-inconsistent problem.
Under certain conditions, we construct an equilibrium strategy which
can be represented via a Riccati--Volterra integral equation system.
Our approach is based on a study of multi-person hierarchical
differential games.
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| 3 |
Global well-posedness and asymptotic behavior of a class of initial-boundary-value problem of the
Korteweg-De Vries equation on a finite domain
Volume 1, Number 1, Pages: 61 - 81, 2011
Ivonne Rivas,
Muhammad Usman
and Bing-Yu Zhang
Abstract
References
Full Text
Related Articles
In this paper, we study a class of initial boundary value problem
(IBVP) of the Korteweg-de Vries equation posed on a finite interval
with nonhomogeneous boundary conditions. The IBVP is known to be
locally well-posed, but its global $L^2$- a priori estimate
is not available and therefore it is not clear whether its solutions
exist globally or blow up in finite time. It is shown in this paper
that the solutions exist globally as long as their initial value and
the associated boundary data are small, and moreover, those
solutions decay exponentially if their boundary data decay
exponentially.
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| 4 |
On the fast solution of evolution equations with a rapidly decaying source term
Volume 1, Number 1, Pages: 1 - 20, 2011
Alain Haraux
Abstract
References
Full Text
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If $L$ is the generator of a uniformly bounded group of operators $T(t)$ on a Banach space $X$, the abstract evolution
equation $ u' + Lu(t) = h(t) $ has a (weak) solution tending to $0$ as
$t\rightarrow +\infty $ if, and only if $\int_0^{+\infty}T(s) h(s) ds $ is semi-convergent, and then this solution is unique.
For the semi-linear equation $ u' + Lu(t) + f(u) = h(t) $, if $f$ such that $f(0) = 0$ is Lipschitz continuous on bounded subsets
of $X$ and has a Lipschitz constant bounded by
$ Cr^\alpha $ in the ball $B(0, r)$ for $r\leq r_0$, for any $h$ satisfiying
$||h(t)|| \leq c(1+t)^{-(1+ \lambda )} $
with $\lambda >\frac{1}{\alpha}$ and $c$ small enough
there exists a unique solution tending to $0$ at least like $(1+t)^{- \lambda}.$ When the system is dissipative,
this special solution makes it sometimes possible to estimate from below the rate of decay to $0$ of the other solutions.
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| 5 |
Rate of $L^2$-concentration of the blow-up solution
for critical nonlinear Schrödinger equation with potential
Volume 1, Number 1, Pages: 119 - 127, 2011
Jian Zhang,
Shihui Zhu
and Xiaoguang Li
Abstract
References
Full Text
Related Articles
We consider the blow-up solutions of the Cauchy problem for the
critical nonlinear Schrödinger equation with a repulsive
harmonic potential. In terms of Merle and Tsutsumi's arguments as
well as Carles' transform, the $L^2$-concentration property of
radially symmetric blow-up solutions is obtained.
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| 6 |
Cesari-type conditions for semilinear elliptic equation with leading term containing controls
Volume 1, Number 1, Pages: 41 - 59, 2011
Bo Li
and Hongwei Lou
Abstract
References
Full Text
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An optimal control problem governed by semilinear elliptic partial
differential equation is considered. The equation is in divergence
form with the leading term containing controls. By studying the
$G$-closure of the leading term, an existence result is established
under a Cesari-type condition.
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| 7 |
Control of a network of magnetic ellipsoidal samples
Volume 1, Number 2, Pages: 129 - 147, 2011
Shruti Agarwal,
Gilles Carbou,
Stéphane Labbé
and Christophe Prieur
Abstract
References
Full Text
Related Articles
In this work, we present a mathematical study of stability and
controllability of one-dimensional network of ferromagnetic
particles. The control is the magnetic field generated by a dipole whose position and whose amplitude can be selected. The evolution of the magnetic field in the network of particles is described by the Landau-Lifschitz equation. First, we model a network of ellipsoidal shape
ferromagnetic particles. Then, we prove the stability of relevant
configurations and discuss the controllability by the means of the
external magnetic field induced by the magnetic dipole.
Finally some
numerical results illustrate the stability and the controllability results.
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| 8 |
Global Carleman inequalities for Stokes and penalized Stokes equations
Volume 1, Number 2, Pages: 149 - 175, 2011
Mehdi Badra
Abstract
References
Full Text
Related Articles
In this note we use the result of [22] to prove a global Carleman inequality related to the null controllability of penalized Stokes kind systems. The constants of the obtained Carleman inequality are uniform in terms of the penalization parameter $\varepsilon$. It then provides a null control with a uniformly (in $\varepsilon$) bounded $L^2$ norm. With a limiting argument we also deduce a new Carleman inequality for Stokes type system. Thus, we apply theses results to obtain the null controllability of Oseen and Navier-Stokes system in the penalized and in the non penalized cases.
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| 9 |
Observability of heat processes by transmutation without geometric restrictions
Volume 1, Number 2, Pages: 177 - 187, 2011
Sylvain Ervedoza
and Enrique Zuazua
Abstract
References
Full Text
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The goal of this note is to explain how transmutation techniques (originally introduced in [14] in the context of the control of the heat equation, inspired on the classical Kannai transform, and recently revisited in [4] and adapted to deal with observability problems) can be applied to derive observability results for the heat equation without any geometric restriction on the subset in which the control is being applied, from a good understanding of the wave equation. Our arguments are based on the recent results in [15] on the frequency depending observability inequalities for waves without geometric restrictions, an iteration argument recently developed in [13] and the new representation formulas in [4] allowing to make a link between heat and wave trajectories.
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| 10 |
Exact controllability of a multilayer Rao-Nakra plate with free boundary conditions
Volume 1, Number 2, Pages: 189 - 230, 2011
Scott W. Hansen
and Oleg Yu Imanuvilov
Abstract
References
Full Text
Related Articles
Exact controllability of a multilayer plate system
with free boundary conditions are
obtained by the method of Carleman estimates. The multilayer plate system
is a natural multilayer generalization of a three-layer "sandwich
plate'' system due to Rao and Nakra. In the multilayer version, $m$
shear deformable layers alternate with $m+1$ layers modeled under
Kirchoff plate assumptions. The resulting system involves $m+1$
Lamé systems coupled with a scalar Kirchhoff plate equation. The
controls are taken to be distributed in a neighborhood of the boundary.
This paper is the sequel to [2] in which only clamped and hinged boundary conditions are considered.
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