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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.
The journal adheres to the publication ethics and malpractice policies outlined by COPE.
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TOP 10 Most Read Articles in MCRF, July 2016
1 
Clarke directional derivatives of regularized gap functions for nonsmooth quasivariational inequalities
Volume 4, Number 3, Pages: 365  379, 2014
Haisen Zhang
Abstract
References
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In optimization problems, it is significant to study the directional
derivatives and subdifferentials of objective functions. Using
directional derivatives and subdifferentials of objective functions,
we can establish optimality conditions, derive error bound
properties, and propose optimal algorithms. In this paper, the upper
and lower estimates for the Clarke directional derivatives of a
class of marginal functions are established. Employing this result,
we obtain the exact formulations of the Clarke directional
derivatives of the regularized gap functions for nonsmooth
quasivariational inequalities.

2 
Existence theory of capillarygravity waves on water of finite depth
Volume 4, Number 3, Pages: 315  363, 2014
ShuMing Sun
Abstract
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This review article discusses the recent developments on the existence of twodimensional and threedimensional capillarygravity
waves on water of finitedepth. The Kortewegde Vries (KdV) equation and KadomtsevPetviashvili (KP) equation
are derived formally from the exact governing equations and the
solitarywave solutions and other solution are obtained for these model equations. Recent results on the
existence of solutions of the exact governing equations near the
solutions of these model equations are presented and various two and
threedimensional solutions of the exact equations are provided. The ideas and
methods to obtain the existence results are briefly discussed.

3 
Optimal insurance in a changing economy
Volume 4, Number 2, Pages: 187  202, 2014
Jingzhen Liu,
KaFai Cedric Yiu,
Tak Kuen Siu
and WaiKi Ching
Abstract
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We discuss a general problem of optimal strategies for insurance,
consumption and investment in a changing economic environment
described by a continuoustime regime switching model. We consider the situation
of a random investment horizon which depends on the
force of mortality of an economic agent. The objective of the agent
is to maximize the expected discounted utility of consumption
and terminal wealth over a random future lifetime. A verification theorem for the HamiltonJacobiBellman (HJB) solution related to the optimal consumption,
investment and insurance is provided. In the cases
of a power utility and an exponential utility, we derive
analytical solutions to the optimal strategies.
Numerical results are given to illustrate the proposed model
and to document the impact of switching regimes on
the optimal strategies.

4 
Time optimal control problems for some nonsmooth systems
Volume 4, Number 3, Pages: 289  314, 2014
Hongwei Lou,
Junjie Wen
and Yashan Xu
Abstract
References
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Time optimal control problems for some nonsmooth systems in general form are considered. The nonsmoothness is caused by singularity. It is proved that Pontryagin's maximum principle holds for at least one optimal relaxed control. Thus, Pontryagin's maximum principle holds when the optimal classical control is a unique optimal relaxed control. By constructing an auxiliary controlled system which admits the original optimal classical control as its unique optimal relaxed control, one get a chance to get Pontryagin's maximum principle for the original optimal classical control. Existence results are also considered.

5 
Null controllability of retarded parabolic equations
Volume 4, Number 1, Pages: 1  15, 2013
Farid Ammar Khodja,
Cherif Bouzidi,
Cédric Dupaix
and Lahcen Maniar
Abstract
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We address in this work the null controllability problem for a linear heat
equation with delay parameters. The control is exerted on a subdomain and we show how
the global Carleman estimate due to Fursikov and Imanuvilov can be applied
to derive results in this direction.

6 
Control of a Kortewegde Vries equation: A tutorial
Volume 4, Number 1, Pages: 45  99, 2013
Eduardo Cerpa
Abstract
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These notes are intended to be a tutorial material revisiting in an almost selfcontained way, some control results for the Kortewegde Vries (KdV) equation posed on a bounded interval. We address the topics of boundary controllability and internal stabilization for this nonlinear control system. Concerning controllability, homogeneous Dirichlet boundary conditions are considered and a control is put on the Neumann boundary condition at the right endpoint of the interval. We show the existence of some critical domains for which the linear KdV equation is not controllable. In despite of that, we prove that in these cases the nonlinearity gives the exact controllability. Regarding stabilization, we study the problem where all the boundary conditions are homogeneous. We add an internal damping mechanism in order to force the solutions of the KdV equation to decay exponentially to the origin in $L^2$norm.

7 
Approximate controllability conditions for some linear 1D parabolic systems with spacedependent coefficients
Volume 4, Number 3, Pages: 263  287, 2014
Franck Boyer
and Guillaume Olive
Abstract
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In this article we are interested in the controllability with one single control force of parabolic systems with spacedependent zeroorder coupling terms. We particularly want to emphasize that, surprisingly enough for parabolic problems, the geometry of the control domain can have an important influence on the controllability properties of the system, depending on the structure of the coupling terms.
Our analysis is mainly based on a criterion given by Fattorini in [12] (and systematically used in [22] for instance), that reduces the problem to the study of a unique continuation property for elliptic systems.
We provide several detailed examples of controllable and noncontrollable systems.
This work gives theoretical justifications of some numerical observations described in [9].

8 
Approximations of infinite dimensional disturbance decoupling and almost disturbance decoupling problems
Volume 4, Number 3, Pages: 381  399, 2014
Xiuxiang Zhou
Abstract
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This paper is addressed to the disturbance decoupling and almost
disturbance decoupling problems in infinite dimensions. We introduce
a class of approximate finite dimensional systems, and show that if
the systems are disturbance decoupled, so does the original infinite
dimensional system. It is also shown that this approach can be
employed to solve the almost disturbance decoupling problem.
Finally, some illustrative examples are provided.

9 
Internal control of the Schrödinger equation
Volume 4, Number 2, Pages: 161  186, 2014
Camille Laurent
Abstract
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In this paper, we intend to present some already known results about the internal controllability of the linear and nonlinear Schrödinger equations.
After presenting the basic properties of the equation, we give a self contained proof of the controllability in dimension $1$ using some propagation results. We then discuss how to obtain some similar results on a compact manifold where the zone of control satisfies the Geometric Control Condition. We also discuss some known results and open questions when this condition is not satisfied.
Then, we present the links between the controllability and some resolvent estimates. Finally, we discuss the additional difficulties when we consider the nonlinear Schrödinger equation.

10 
Local controllability of 1D Schrödinger equations with bilinear control and minimal time
Volume 4, Number 2, Pages: 125  160, 2014
Karine Beauchard
and Morgan Morancey
Abstract
References
Full Text
Related Articles
We consider a linear Schrödinger equation, on a bounded interval, with bilinear control.
In [10], Beauchard and Laurent prove that, under an appropriate non degeneracy assumption,
this system is controllable, locally around the ground state, in arbitrary time.
In [18], Coron proves that a positive minimal time is required for this controllability result,
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.

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