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

2 
Stabilization of hyperbolic equations with mixed boundary conditions
Volume 5, Number 4, Pages: 761  780, 2015
Xiaoyu Fu
Abstract
References
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This paper is devoted to study decay properties of solutions to hyperbolic equations in a bounded domain with two types of dissipative mechanisms, i.e. either with a small boundary or an internal damping. Both of the equations are equipped with the mixed boundary conditions. When the Geometric Control Condition on the dissipative region is not satisfied, we show that sufficiently smooth solutions to the equations decay logarithmically, under sharp regularity assumptions on the coefficients, the damping and the boundary of the domain involved in the equations. Our decay results rely on an analysis of the size of resolvent operators for hyperbolic equations on the imaginary axis. To derive this kind of resolvent estimates, we employ global Carleman estimates for elliptic equations with mixed boundary conditions.

3 
Exact controllability for the Lamé system
Volume 5, Number 4, Pages: 743  760, 2015
Belhassen Dehman
and JeanPierre Raymond
Abstract
References
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In this article, we prove an exact boundary controllability result for the isotropic elastic wave system in a bounded domain $\Omega$ of $\mathbb{R}^{3}$. This result is obtained under a microlocal condition linking the bicharacteristic paths of the system and the region of the boundary on which the control acts. This condition is to be compared with the socalled Geometric Control Condition by Bardos, Lebeau and Rauch [3]. The proof relies on microlocal tools, namely the propagation of the $C^{\infty}$ wave front and microlocal defect measures.

4 
Finitetime stabilization of a network of strings
Volume 5, Number 4, Pages: 721  742, 2015
Fatiha AlabauBoussouira,
Vincent Perrollaz
and Lionel Rosier
Abstract
References
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We investigate the finitetime stabilization of a treeshaped network of strings. Transparent boundary conditions are applied at all the external nodes.
At any internal node, in addition to the usual continuity conditions, a modified Kirchhoff law incorporating a damping term $\alpha u_t$ with a
coefficient $\alpha$ that may depend on the node is considered.
We show that for a convenient choice of the sequence of coefficients $\alpha$, any solution of the wave equation on the network becomes constant
after a finite time. The condition on the coefficients proves to be sharp at least for a starshaped tree. Similar results are derived when we replace the transparent
boundary condition by the Dirichlet (resp. Neumann) boundary condition at one external node. Our results lead to the finitetime stabilization even
though the systems may not be dissipative.

5 
Adaptive projective synchronization of memristive neural networks with timevarying delays and stochastic perturbation
Volume 5, Number 4, Pages: 827  844, 2015
Ruoxia Li,
Huaiqin Wu,
Xiaowei Zhang
and Rong Yao
Abstract
References
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This paper is concerned with the projective synchronization issue
for memristive neural networks with timevarying delays and
stochastic perturbations. Based on LaSalletype invariance
principle of stochastic functionaldifferential equations, by
applying Lyapunov functional approach, several sufficient
conditions are developed to achieve the projective synchronization
between the masterslave systems with timevarying delays under
stochastic perturbation and adaptive controller. A numerical
example and its simulation is given to show the effectiveness of
the theoretical results in this paper.

6 
Generalized homogeneous systems with applications to nonlinear control: A survey
Volume 5, Number 3, Pages: 585  611, 2015
Chunjiang Qian,
Wei Lin
and Wenting Zha
Abstract
References
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This survey provides a unified homogeneous perspective on recent advances in the global stabilization of various nonlinear systems with uncertainty. We first review definitions and properties of homogeneous systems and illustrate how the homogeneous system theory can yield elegant feedback stabilizers for certain homogeneous systems. By taking advantage of homogeneity, we then present the socalled Adding a Power Integrator (AAPI) technique and discuss how it can be employed to recursively construct smooth state feedback stabilizers for uncertain nonlinear systems with uncontrollable linearizations. Based on the AAPI technique, a nonsmooth version as well as a generalized version of AAPI approaches can be further developed from a homogeneous viewpoint, resulting in solutions to the global stabilization of genuinely nonlinear systems that may not be controlled, even locally, by any smooth state feedback. In the case of output feedback control, we demonstrate in this survey why the homogeneity is the key in developing a homogeneous domination approach, which has been successful in solving some difficult nonlinear control problems including, for instance, the global stabilization of systems with higherorder nonlinearities via output feedback. Finally, we show how the notion of Homogeneity with Monotone Degrees (HWMD) plays a decisive role in unifying smooth and nonsmooth AAPI methods under one framework. Other
applications of HWMD will be also summarized and discussed in this paper, along the directions of constructing smooth stabilizers for nonlinear systems in special forms and ``lowgain'' controllers for a class of general uppertriangular systems.

7 
Stochastic recursive optimal control problem with time delay and applications
Volume 5, Number 4, Pages: 859  888, 2015
Jingtao Shi,
Juanjuan Xu
and Huanshui Zhang
Abstract
References
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This paper is concerned with a stochastic recursive optimal control problem with time delay, where the controlled system is described by a stochastic differential delayed equation (SDDE) and the cost functional is formulated as the solution to a backward SDDE (BSDDE). When there are only the pointwise and distributed time delays in the state variable, a generalized HamiltonJacobiBellman (HJB) equation for the value function in finite dimensional space is obtained, applying dynamic programming principle. This generalized HJB equation admits a smooth solution when the coefficients satisfy a particular system of first order partial differential equations (PDEs). A sufficient maximum principle is derived, where the adjoint equation is a forwardbackward SDDE (FBSDDE). Under some differentiability assumptions, the relationship between the value function, the adjoint processes and the generalized Hamiltonian function is obtained. A consumption and portfolio optimization problem with recursive utility in the financial market, is discussed to show the applications of our result. Explicit solutions in a finite dimensional space derived by the two different approaches, coincide.

8 
Pairs trading: An optimal selling rule
Volume 5, Number 3, Pages: 489  499, 2015
Kevin Kuo,
Phong Luu,
Duy Nguyen,
Eric Perkerson,
Katherine Thompson
and Qing Zhang
Abstract
References
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Pairs trading involves two cointegrated securities.
When divergence is underway, i.e., one stock moves up while the other
moves down, a pairs trade is entered consisting of
a short position in the outperforming stock and a long
position in the underperforming one.
Such a strategy bets the ``spread'' between the two would eventually
converge.
This paper is concerned with an optimal pairstrade selling rule.
In this paper, a difference of the pair is governed by a meanreverting
model. The trade will be closed whenever the difference reaches a
target level or a cutloss limit. Given a fixed cutloss level,
the objective is to determine the optimal target
so as to maximize an overall return.
This optimization problem is related to an optimal stopping problem
as the cutloss level vanishes.
Expected holding time and profit probability are also obtained.
Numerical examples are reported to demonstrate the results.

9 
Signerror adaptive filtering algorithms involving Markovian parameters
Volume 5, Number 4, Pages: 781  806, 2015
Araz Hashemi,
George Yin
and Le Yi Wang
Abstract
References
Full Text
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Motivated by reduction of computational complexity,
this work develops signerror adaptive filtering algorithms for estimating
randomly timevarying
system
parameters.
Different from the existing work on signerror algorithms,
the parameters are timevarying and their dynamics are modeled by a discretetime
Markov chain.
Another distinctive feature of the algorithms is the
multitimescale framework for characterizing parameter variations and algorithm updating speeds.
This is realized by considering the stepsize of the estimation algorithms and
a scaling parameter that defines the transition rate of the Markov
jump process. Depending on the relative time scales of these two processes, suitably scaled sequences
of the estimates
are shown to converge to either an
ordinary differential equation, or a set of ordinary differential equations modulated by random switching, or
a stochastic differential equation,
or stochastic differential equations with random switching. Using weak convergence methods, convergence and rates of convergence of the algorithms
are obtained for all these cases. Simulation results are provided for demonstration.

10 
Sparse initial data identification for parabolic PDE and its finite element approximations
Volume 5, Number 3, Pages: 377  399, 2015
Eduardo Casas,
Boris Vexler
and Enrique Zuazua
Abstract
References
Full Text
Related Articles
We address the problem of inverse source identification for parabolic equations from the optimal control viewpoint employing measures of minimal norm as initial data. We adopt the point of view of approximate controllability so that the target is not required to be achieved exactly but only in an approximate sense. We prove an approximate inversion result and derive a characterization of the optimal initial measures by means of duality and the minimization of a suitable quadratic functional on the solutions of the adjoint system. We prove the sparsity of the optimal initial measures showing that they are supported in sets of null Lebesgue measure. As a consequence, approximate controllability can be achieved efficiently by means of controls that are activated in a finite number of pointwise locations. Moreover, we discuss the finite element numerical approximation of the control problem providing a convergence result of the corresponding optimal measures and states as the discretization parameters tend to zero.

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