ISSN:
 2156-8472

eISSN:
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Volume 7, 2017

Volume 6, 2016

Volume 5, 2015

Volume 4, 2014

Volume 3, 2013

Volume 2, 2012

Volume 1, 2011

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.

  • AIMS is a member of COPE. All AIMS journals adhere to the publication ethics and malpractice policies outlined by COPE.
  • Publishes 4 issues a year in March, June, September and December.
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  • MCRF is a publication of the American Institute of Mathematical Sciences. All rights reserved.

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Necessary conditions for a weak minimum in a general optimal control problem with integral equations on a variable time interval
Andrei V. Dmitruk  and  Nikolai P. Osmolovski 
2017, 7(4) : 507-535 doi: 10.3934/mcrf.2017019 +[Abstract](92) +[HTML](0) +[PDF](452.1KB)
Abstract:

We study an optimal control problem with a nonlinear Volterra-type integral equation considered on a nonfixed time interval, subject to endpoint constraints of equality and inequality type, mixed state-control constraints of inequality and equality type, and pure state constraints of inequality type. The main assumption is the linear–positive independence of the gradients of active mixed constraints with respect to the control. We obtain first-order necessary optimality conditions for an extended weak minimum, the notion of which is a natural generalization of the notion of weak minimum with account of variations of the time. The conditions obtained generalize the corresponding ones for problems with ordinary differential equations.

Controllability of fractional dynamical systems: A functional analytic approach
Venkatesan Govindaraj  and  Raju K. George 
2017, 7(4) : 537-562 doi: 10.3934/mcrf.2017020 +[Abstract](66) +[HTML](0) +[PDF](452.1KB)
Abstract:

In this paper, we investigate controllability of fractional dynamical systems involving monotone nonlinearities of both Lipchitzian and non-Lipchitzian types. We invoke tools of nonlinear analysis like fixed point theorem and monotone operator theory to obtain controllability results for the nonlinear system. Examples are provided to illustrate the results. Controllability results of fractional dynamical systems with monotone nonlinearity is new.

A stochastic control problem and related free boundaries in finance
Chonghu Guan  , Xun Li  , Zuo Quan Xu  and  Fahuai Yi 
2017, 7(4) : 563-584 doi: 10.3934/mcrf.2017021 +[Abstract](54) +[HTML](0) +[PDF](452.1KB)
Abstract:

In this paper, we investigate an optimal stopping problem (mixed with stochastic controls) for a manager whose utility is nonsmooth and nonconcave over a finite time horizon. The paper aims to develop a new methodology, which is significantly different from those of mixed dynamic optimal control and stopping problems in the existing literature, so as to figure out the manager's best strategies. The problem is first reformulated into a free boundary problem with a fully nonlinear operator. Then, by means of a dual transformation, it is further converted into a free boundary problem with a linear operator, which can be consequently tackled by the classical method. Finally, using the inverse transformation, we obtain the properties of the optimal trading strategy and the optimal stopping time for the original problem.

Time-inconsistent optimal control problems with regime-switching
Jiaqin Wei 
2017, 7(4) : 585-622 doi: 10.3934/mcrf.2017022 +[Abstract](84) +[HTML](4) +[PDF](637.7KB)
Abstract:

In this paper, a time-inconsistent optimal control problem is studied for diffusion processes modulated by a continuous-time Markov chain. In the performance functional, the running cost and terminal cost depend on not only the initial time, but also the initial state of the Markov chain. By modifying the method of multi-person game, we obtain an equilibrium Hamilton-Jacobi-Bellman equation under proper conditions. The well-posedness of this equilibrium HJB Equation is studied in the case where the diffusion term is independent of the control variable. Furthermore, a time-inconsistent linear-quadratic control problem is considered as a special case.

Addendum to "A sparse Markov chain approximation of LQ-type stochastic control problems"
Ralf Banisch  and  Carsten Hartmann 
2017, 7(4) : 623-623 doi: 10.3934/mcrf.2017023 +[Abstract](49) +[HTML](0) +[PDF](132.1KB)
Abstract:
Inverse source problem with a final overdetermination for a fractional diffusion equation
Kenichi Sakamoto  and  Masahiro Yamamoto 
2011, 1(4) : 509-518 doi: 10.3934/mcrf.2011.1.509 +[Abstract](66) +[PDF](316.6KB) Cited By(23)
Strict Lyapunov functions for semilinear parabolic partial differential equations
Frédéric Mazenc  and  Christophe Prieur 
2011, 1(2) : 231-250 doi: 10.3934/mcrf.2011.1.231 +[Abstract](57) +[PDF](929.8KB) Cited By(18)
Sparse stabilization and optimal control of the Cucker-Smale model
Marco Caponigro  , Massimo Fornasier  , Benedetto Piccoli  and  Emmanuel Trélat 
2013, 3(4) : 447-466 doi: 10.3934/mcrf.2013.3.447 +[Abstract](63) +[PDF](467.3KB) Cited By(18)
A linear-quadratic optimal control problem for mean-field stochastic differential equations in infinite horizon
Jianhui Huang  , Xun Li  and  Jiongmin Yong 
2015, 5(1) : 97-139 doi: 10.3934/mcrf.2015.5.97 +[Abstract](78) +[PDF](614.2KB) Cited By(13)
A deterministic linear quadratic time-inconsistent optimal control problem
Jiongmin Yong 
2011, 1(1) : 83-118 doi: 10.3934/mcrf.2011.1.83 +[Abstract](65) +[PDF](442.3KB) Cited By(12)
Time-inconsistent optimal control problems and the equilibrium HJB equation
Jiongmin Yong 
2012, 2(3) : 271-329 doi: 10.3934/mcrf.2012.2.271 +[Abstract](67) +[PDF](637.9KB) Cited By(11)
Control of a Korteweg-de Vries equation: A tutorial
Eduardo Cerpa 
2014, 4(1) : 45-99 doi: 10.3934/mcrf.2014.4.45 +[Abstract](59) +[PDF](701.7KB) Cited By(11)
Global well-posedness and asymptotic behavior of a class of initial-boundary-value problem of the Korteweg-De Vries equation on a finite domain
Ivonne Rivas  , Muhammad Usman  and  Bing-Yu Zhang 
2011, 1(1) : 61-81 doi: 10.3934/mcrf.2011.1.61 +[Abstract](52) +[PDF](455.9KB) Cited By(11)
Time-delayed boundary feedback stabilization of the isothermal Euler equations with friction
Martin Gugat  and  Markus Dick 
2011, 1(4) : 469-491 doi: 10.3934/mcrf.2011.1.469 +[Abstract](49) +[PDF](368.5KB) Cited By(10)
Stability estimates for a Robin coefficient in the two-dimensional Stokes system
Muriel Boulakia  , Anne-Claire Egloffe  and  Céline Grandmont 
2013, 3(1) : 21-49 doi: 10.3934/mcrf.2013.3.21 +[Abstract](54) +[PDF](695.4KB) Cited By(8)
A linear-quadratic optimal control problem for mean-field stochastic differential equations in infinite horizon
Jianhui Huang  , Xun Li  and  Jiongmin Yong 
2015, 5(1) : 97-139 doi: 10.3934/mcrf.2015.5.97 +[Abstract](78) +[PDF](614.2KB) PDF Downloads(4)
Optimal control of a vector-host epidemics model
Qingkai Kong  , Zhipeng Qiu  , Zi Sang  and  Yun Zou 
2011, 1(4) : 493-508 doi: 10.3934/mcrf.2011.1.493 +[Abstract](49) +[PDF](556.4KB) PDF Downloads(4)
Stability and controllability of a wave equation with dynamical boundary control
Bopeng Rao  , Laila Toufayli  and  Ali Wehbe 
2015, 5(2) : 305-320 doi: 10.3934/mcrf.2015.5.305 +[Abstract](51) +[PDF](389.5KB) PDF Downloads(3)
Exact controllability of scalar conservation laws with strict convex flux
Adimurthi   , Shyam Sundar Ghoshal  and  G. D. Veerappa Gowda 
2014, 4(4) : 401-449 doi: 10.3934/mcrf.2014.4.401 +[Abstract](92) +[PDF](657.7KB) PDF Downloads(3)
Exact controllability for the Lamé system
Belhassen Dehman  and  Jean-Pierre Raymond 
2015, 5(4) : 743-760 doi: 10.3934/mcrf.2015.5.743 +[Abstract](186) +[PDF](428.1KB) PDF Downloads(3)
Existence of optimal solutions to Lagrange problem for a fractional nonlinear control system with Riemann-Liouville derivative
Dariusz Idczak  and  Rafał Kamocki 
2017, 7(3) : 449-464 doi: 10.3934/mcrf.2017016 +[Abstract](220) +[HTML](3) +[PDF](480.0KB) PDF Downloads(3)
On the convergence of the Sakawa-Shindo algorithm in stochastic control
J. Frédéric Bonnans  , Justina Gianatti  and  Francisco J. Silva 
2016, 6(3) : 391-406 doi: 10.3934/mcrf.2016008 +[Abstract](48) +[PDF](451.6KB) PDF Downloads(2)
Optimal control of a multi-level dynamic model for biofuel production
Roberta Ghezzi  and  Benedetto Piccoli 
2017, 7(2) : 235-257 doi: 10.3934/mcrf.2017008 +[Abstract](67) +[HTML](0) +[PDF](484.6KB) PDF Downloads(2)
Time-inconsistent optimal control problem with random coefficients and stochastic equilibrium HJB equation
Haiyang Wang  and  Zhen Wu 
2015, 5(3) : 651-678 doi: 10.3934/mcrf.2015.5.651 +[Abstract](168) +[PDF](438.3KB) PDF Downloads(2)
Pairs trading: An optimal selling rule
Kevin Kuo  , Phong Luu  , Duy Nguyen  , Eric Perkerson  , Katherine Thompson  and  Qing Zhang 
2015, 5(3) : 489-499 doi: 10.3934/mcrf.2015.5.489 +[Abstract](136) +[PDF](335.5KB) PDF Downloads(2)

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