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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.


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Quantitative approximation properties for the fractional heat equation
Angkana Rüland and Mikko Salo
2020, 10(1) : 1-26 doi: 10.3934/mcrf.2019027 +[Abstract](990) +[HTML](463) +[PDF](421.41KB)
A Poincaré-Bendixson theorem for hybrid systems
William Clark, Anthony Bloch and Leonardo Colombo
2020, 10(1) : 27-45 doi: 10.3934/mcrf.2019028 +[Abstract](1018) +[HTML](565) +[PDF](585.77KB)
Time minimal saturation of a pair of spins and application in Magnetic Resonance Imaging
Bernard Bonnard, Olivier Cots, Jérémy Rouot and Thibaut Verron
2020, 10(1) : 47-88 doi: 10.3934/mcrf.2019029 +[Abstract](1057) +[HTML](540) +[PDF](1059.52KB)
Minimal time of null controllability of two parabolic equations
Lydia Ouaili
2020, 10(1) : 89-112 doi: 10.3934/mcrf.2019031 +[Abstract](1064) +[HTML](477) +[PDF](235.37KB)
A moment approach for entropy solutions to nonlinear hyperbolic PDEs
Swann Marx, Tillmann Weisser, Didier Henrion and Jean Bernard Lasserre
2020, 10(1) : 113-140 doi: 10.3934/mcrf.2019032 +[Abstract](1191) +[HTML](474) +[PDF](677.52KB)
Regional gradient controllability of ultra-slow diffusions involving the Hadamard-Caputo time fractional derivative
Ruiyang Cai, Fudong Ge, Yangquan Chen and Chunhai Kou
2020, 10(1) : 141-156 doi: 10.3934/mcrf.2019033 +[Abstract](1048) +[HTML](485) +[PDF](374.39KB)
Controllability properties of degenerate pseudo-parabolic boundary control problems
Mu-Ming Zhang, Tian-Yuan Xu and Jing-Xue Yin
2020, 10(1) : 157-169 doi: 10.3934/mcrf.2019034 +[Abstract](1172) +[HTML](522) +[PDF](338.24KB)
A direct method based on the Clenshaw-Curtis formula for fractional optimal control problems
Mohammad Hadi Noori Skandari, Marzieh Habibli and Alireza Nazemi
2020, 10(1) : 171-187 doi: 10.3934/mcrf.2019035 +[Abstract](519) +[HTML](287) +[PDF](537.44KB)
Stable reconstruction of the volatility in a regime-switching local-volatility model
Mourad Bellassoued, Raymond Brummelhuis, Michel Cristofol and Éric Soccorsi
2020, 10(1) : 189-215 doi: 10.3934/mcrf.2019036 +[Abstract](475) +[HTML](202) +[PDF](483.58KB)
Boundary null-controllability of semi-discrete coupled parabolic systems in some multi-dimensional geometries
Damien Allonsius and Franck Boyer
2019doi: 10.3934/mcrf.2019037 +[Abstract](469) +[HTML](200) +[PDF](1848.14KB)
Free boundaries of credit rating migration in switching macro regions
Yuan Wu and Jin Liang
2019doi: 10.3934/mcrf.2019038 +[Abstract](409) +[HTML](221) +[PDF](1197.38KB)
On the exact controllability and the stabilization for the Benney-Luke equation
José R. Quintero and Alex M. Montes
2019doi: 10.3934/mcrf.2019039 +[Abstract](484) +[HTML](287) +[PDF](443.35KB)
Optimal treatment for a phase field system of Cahn-Hilliard type modeling tumor growth by asymptotic scheme
Andrea Signori
2019doi: 10.3934/mcrf.2019040 +[Abstract](496) +[HTML](214) +[PDF](389.64KB)
Finite element error estimates for one-dimensional elliptic optimal control by BV-functions
Dominik Hafemeyer, Florian Mannel, Ira Neitzel and Boris Vexler
2019doi: 10.3934/mcrf.2019041 +[Abstract](538) +[HTML](236) +[PDF](551.88KB)
Optimal investment problem with delay under partial information
Shuaiqi Zhang, Jie Xiong and Xin Zhang
2019doi: 10.3934/mcrf.2020001 +[Abstract](214) +[HTML](83) +[PDF](368.05KB)
Necessary condition for optimal control of doubly stochastic systems
Liangquan Zhang, Qing Zhou and Juan Yang
2019doi: 10.3934/mcrf.2020002 +[Abstract](229) +[HTML](110) +[PDF](377.36KB)
Feedback stabilization for a coupled PDE-ODE production system
Vanessa Baumgärtner, Simone Göttlich and Stephan Knapp
2019doi: 10.3934/mcrf.2020003 +[Abstract](203) +[HTML](109) +[PDF](883.23KB)
Singular control of SPDEs with space-mean dynamics
Nacira Agram, Astrid Hilbert and Bernt Øksendal
2019doi: 10.3934/mcrf.2020004 +[Abstract](158) +[HTML](100) +[PDF](325.08KB)
Switching controls for linear stochastic differential systems
Yong He
2019doi: 10.3934/mcrf.2020005 +[Abstract](186) +[HTML](109) +[PDF](277.07KB)
Implicit parametrizations and applications in optimization and control
Dan Tiba
2019doi: 10.3934/mcrf.2020006 +[Abstract](160) +[HTML](77) +[PDF](479.5KB)
Sparse optimal control for the heat equation with mixed control-state constraints
Eduardo Casas and Fredi Tröltzsch
2019doi: 10.3934/mcrf.2020007 +[Abstract](149) +[HTML](70) +[PDF](350.47KB)
Optimality conditions in variational form for non-linear constrained stochastic control problems
Laurent Pfeiffer
2019doi: 10.3934/mcrf.2020008 +[Abstract](116) +[HTML](54) +[PDF](601.4KB)
State-constrained semilinear elliptic optimization problems with unrestricted sparse controls
Eduardo Casas and Fredi Tröltzsch
2019doi: 10.3934/mcrf.2020009 +[Abstract](144) +[HTML](74) +[PDF](362.64KB)
Optimal periodic control for scalar dynamics under integral constraint on the input
Térence Bayen, Alain Rapaport and Fatima-Zahra Tani
2019doi: 10.3934/mcrf.2020010 +[Abstract](134) +[HTML](77) +[PDF](412.43KB)
A convergent hierarchy of non-linear eigenproblems to compute the joint spectral radius of nonnegative matrices
Stéphane Gaubert and Nikolas Stott
2019doi: 10.3934/mcrf.2020011 +[Abstract](142) +[HTML](81) +[PDF](335.49KB)
Optimal control of the linear wave equation by time-depending BV-controls: A semi-smooth Newton approach
Sebastian Engel and Karl Kunisch
2019doi: 10.3934/mcrf.2020012 +[Abstract](149) +[HTML](76) +[PDF](716.04KB)
Controllability of a system of degenerate parabolic equations with non-diagonalizable diffusion matrix
El Mustapha Ait Ben Hassi, Mohamed Fadili and Lahcen Maniar
2019doi: 10.3934/mcrf.2020013 +[Abstract](152) +[HTML](53) +[PDF](437.55KB)
Lipschitz stability for some coupled degenerate parabolic systems with locally distributed observations of one component
Brahim Allal, Abdelkarim Hajjaj, Lahcen Maniar and Jawad Salhi
2019doi: 10.3934/mcrf.2020014 +[Abstract](206) +[HTML](98) +[PDF](425.63KB)
Uniform indirect boundary controllability of semi-discrete $ 1 $-$ d $ coupled wave equations
Abdeladim El Akri and Lahcen Maniar
2019doi: 10.3934/mcrf.2020015 +[Abstract](141) +[HTML](78) +[PDF](535.51KB)
The Kato smoothing effect for the nonlinear regularized Schrödinger equation on compact manifolds
Lassaad Aloui and Imen El Khal El Taief
2019doi: 10.3934/mcrf.2020016 +[Abstract](181) +[HTML](69) +[PDF](336.47KB)
Asymptotic stabilization of continuous-time periodic stochastic systems by feedback control based on periodic discrete-time observations
Ran Dong and Xuerong Mao
2019doi: 10.3934/mcrf.2020017 +[Abstract](137) +[HTML](64) +[PDF](489.97KB)
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](2887) +[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](2509) +[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](2927) +[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](2936) +[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](20004) +[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](2923) +[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](2497) +[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](3187) +[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](2422) +[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](2414) +[PDF](695.4KB) Cited By(8)
Optimal control of the coefficient for the regional fractional $p$-Laplace equation: Approximation and convergence
Harbir Antil and Mahamadi Warma
2019, 9(1) : 1-38 doi: 10.3934/mcrf.2019001 +[Abstract](3000) +[HTML](805) +[PDF](617.03KB) PDF Downloads(254)
Extension of the strong law of large numbers for capacities
Zengjing Chen, Weihuan Huang and Panyu Wu
2019, 9(1) : 175-190 doi: 10.3934/mcrf.2019010 +[Abstract](2558) +[HTML](667) +[PDF](403.95KB) PDF Downloads(223)
Asymptotic behavior of a Schrödinger equation under a constrained boundary feedback
Haoyue Cui, Dongyi Liu and Genqi Xu
2018, 8(2) : 383-395 doi: 10.3934/mcrf.2018015 +[Abstract](3551) +[HTML](517) +[PDF](434.73KB) PDF Downloads(210)
Robust optimal investment and reinsurance of an insurer under Jump-diffusion models
Xin Zhang, Hui Meng, Jie Xiong and Yang Shen
2019, 9(1) : 59-76 doi: 10.3934/mcrf.2019003 +[Abstract](3235) +[HTML](1087) +[PDF](526.9KB) PDF Downloads(201)
Quantitative approximation properties for the fractional heat equation
Angkana Rüland and Mikko Salo
2020, 10(1) : 1-26 doi: 10.3934/mcrf.2019027 +[Abstract](990) +[HTML](463) +[PDF](421.41KB) PDF Downloads(188)
Linear quadratic mean-field-game of backward stochastic differential systems
Kai Du, Jianhui Huang and Zhen Wu
2018, 8(3&4) : 653-678 doi: 10.3934/mcrf.2018028 +[Abstract](2974) +[HTML](457) +[PDF](514.51KB) PDF Downloads(137)
A moment approach for entropy solutions to nonlinear hyperbolic PDEs
Swann Marx, Tillmann Weisser, Didier Henrion and Jean Bernard Lasserre
2020, 10(1) : 113-140 doi: 10.3934/mcrf.2019032 +[Abstract](1191) +[HTML](474) +[PDF](677.52KB) PDF Downloads(134)
A partially observed non-zero sum differential game of forward-backward stochastic differential equations and its application in finance
Jie Xiong, Shuaiqi Zhang and Yi Zhuang
2019, 9(2) : 257-276 doi: 10.3934/mcrf.2019013 +[Abstract](2290) +[HTML](686) +[PDF](430.53KB) PDF Downloads(133)
Second order optimality conditions for optimal control of quasilinear parabolic equations
Lucas Bonifacius and Ira Neitzel
2018, 8(1) : 1-34 doi: 10.3934/mcrf.2018001 +[Abstract](4545) +[HTML](347) +[PDF](640.17KB) PDF Downloads(133)
On a logarithmic stability estimate for an inverse heat conduction problem
Aymen Jbalia
2019, 9(2) : 277-287 doi: 10.3934/mcrf.2019014 +[Abstract](2002) +[HTML](681) +[PDF](399.46KB) PDF Downloads(131)

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