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The optimal control to restore the periodic property of a linear evolution system with small perturbation
1.  School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China 
[1] 
Hans Josef Pesch. Carathéodory's royal road of the calculus of variations: Missed exits to the maximum principle of optimal control theory. Numerical Algebra, Control and Optimization, 2013, 3 (1) : 161173. doi: 10.3934/naco.2013.3.161 
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Zaidong Zhan, Shuping Chen, Wei Wei. A unified theory of maximum principle for continuous and discrete time optimal control problems. Mathematical Control and Related Fields, 2012, 2 (2) : 195215. doi: 10.3934/mcrf.2012.2.195 
[3] 
Torsten Lindström. Discrete models and Fisher's maximum principle in ecology. Conference Publications, 2003, 2003 (Special) : 571579. doi: 10.3934/proc.2003.2003.571 
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Md. Haider Ali Biswas, Maria do Rosário de Pinho. A nonsmooth maximum principle for optimal control problems with state and mixed constraints  convex case. Conference Publications, 2011, 2011 (Special) : 174183. doi: 10.3934/proc.2011.2011.174 
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Stefan Doboszczak, Manil T. Mohan, Sivaguru S. Sritharan. Pontryagin maximum principle for the optimal control of linearized compressible navierstokes equations with state constraints. Evolution Equations and Control Theory, 2022, 11 (2) : 347371. doi: 10.3934/eect.2020110 
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Zhen Wu, Feng Zhang. Maximum principle for discretetime stochastic optimal control problem and stochastic game. Mathematical Control and Related Fields, 2022, 12 (2) : 475493. doi: 10.3934/mcrf.2021031 
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Yan Wang, Yanxiang Zhao, Lei Wang, Aimin Song, Yanping Ma. Stochastic maximum principle for partial information optimal investment and dividend problem of an insurer. Journal of Industrial and Management Optimization, 2018, 14 (2) : 653671. doi: 10.3934/jimo.2017067 
[8] 
Shanjian Tang. A secondorder maximum principle for singular optimal stochastic controls. Discrete and Continuous Dynamical Systems  B, 2010, 14 (4) : 15811599. doi: 10.3934/dcdsb.2010.14.1581 
[9] 
H. O. Fattorini. The maximum principle for linear infinite dimensional control systems with state constraints. Discrete and Continuous Dynamical Systems, 1995, 1 (1) : 77101. doi: 10.3934/dcds.1995.1.77 
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Shaolin Ji, Xiaole Xue. A stochastic maximum principle for linear quadratic problem with nonconvex control domain. Mathematical Control and Related Fields, 2019, 9 (3) : 495507. doi: 10.3934/mcrf.2019022 
[11] 
Vaibhav Mehandiratta, Mani Mehra, Günter Leugering. Fractional optimal control problems on a star graph: Optimality system and numerical solution. Mathematical Control and Related Fields, 2021, 11 (1) : 189209. doi: 10.3934/mcrf.2020033 
[12] 
Huaiqiang Yu, Bin Liu. Pontryagin's principle for local solutions of optimal control governed by the 2D NavierStokes equations with mixed controlstate constraints. Mathematical Control and Related Fields, 2012, 2 (1) : 6180. doi: 10.3934/mcrf.2012.2.61 
[13] 
H. O. Fattorini. The maximum principle in infinite dimension. Discrete and Continuous Dynamical Systems, 2000, 6 (3) : 557574. doi: 10.3934/dcds.2000.6.557 
[14] 
Erik Kropat. Homogenization of optimal control problems on curvilinear networks with a periodic microstructure Results on $\boldsymbol{S}$homogenization and $\boldsymbol{Γ}$convergence. Numerical Algebra, Control and Optimization, 2017, 7 (1) : 5176. doi: 10.3934/naco.2017003 
[15] 
Miaomiao Chen, Rong Yuan. Maximum principle for the optimal harvesting problem of a sizestagestructured population model. Discrete and Continuous Dynamical Systems  B, 2021 doi: 10.3934/dcdsb.2021245 
[16] 
Hancheng Guo, Jie Xiong. A secondorder stochastic maximum principle for generalized meanfield singular control problem. Mathematical Control and Related Fields, 2018, 8 (2) : 451473. doi: 10.3934/mcrf.2018018 
[17] 
Guy Barles, Ariela Briani, Emmanuel Trélat. Value function for regional control problems via dynamic programming and Pontryagin maximum principle. Mathematical Control and Related Fields, 2018, 8 (3&4) : 509533. doi: 10.3934/mcrf.2018021 
[18] 
Carlo Orrieri. A stochastic maximum principle with dissipativity conditions. Discrete and Continuous Dynamical Systems, 2015, 35 (11) : 54995519. doi: 10.3934/dcds.2015.35.5499 
[19] 
ChiunChuan Chen, TingYang Hsiao, LiChang Hung. Discrete Nbarrier maximum principle for a lattice dynamical system arising in competition models. Discrete and Continuous Dynamical Systems, 2020, 40 (1) : 153187. doi: 10.3934/dcds.2020007 
[20] 
Tian Chen, Zhen Wu. A general maximum principle for partially observed meanfield stochastic system with random jumps in progressive structure. Mathematical Control and Related Fields, 2022 doi: 10.3934/mcrf.2022012 
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