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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 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.
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 Publishes 4 issues a year in March, June, September and December.
 Publishes online only.
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 MCRF is a publication of the American Institute of Mathematical Sciences. All rights reserved.

TOP 10 Most Read Articles in MCRF, October 2017
1 
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.

2 
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.

3 
Generalization on optimal multiple stopping with application to swing options with random exercise rights number
Volume 5, Number 4, Pages: 807  826, 2015
Noureddine Jilani Ben Naouara
and Faouzi Trabelsi
Abstract
References
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This paper develops the theory of optimal multiple stopping times expected value problems by stating, proving, and applying a dynamic programming principle for the case in which both the reward process and the number of stopping times are stochastic. This case comes up in practice when valuing swing options, which are somewhat common in commodity trading. We believe our results significantly advance the study of option pricing.

4 
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
References
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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.

5 
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
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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.

6 
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.

7 
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.

8 
Carleman estimates for semidiscrete parabolic operators with a discontinuous diffusion coefficient and applications to controllability
Volume 4, Number 2, Pages: 203  259, 2014
Thuy N. T. Nguyen
Abstract
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In the discrete setting of onedimensional finitedifferences we prove a Carleman estimate for a semidiscretization of the parabolic operator $\partial_t\partial_x (c\partial_x )$ where the diffusion coefficient $c$ has a jump. As a consequence of this Carleman estimate, we deduce consistent nullcontrollability results for classes of semilinear parabolic equations.

9 
Errata: Controllability of the cubic Schroedinger equation via a lowdimensional source term
Volume 4, Number 2, Pages: 261  261, 2014
Andrey Sarychev
Abstract
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10 
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
References
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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].

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