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A Knesertype theorem for backward doubly stochastic differential equations
A secondorder maximum principle for singular optimal stochastic controls
1.  Department of Finance and Control Sciences, School of Mathematical Sciences, Fudan University, Shanghai 200433, China 
[1] 
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 
[2] 
Doyoon Kim, Seungjin Ryu. The weak maximum principle for secondorder elliptic and parabolic conormal derivative problems. Communications on Pure and Applied Analysis, 2020, 19 (1) : 493510. doi: 10.3934/cpaa.2020024 
[3] 
Leonardo Colombo, David Martín de Diego. Secondorder variational problems on Lie groupoids and optimal control applications. Discrete and Continuous Dynamical Systems, 2016, 36 (11) : 60236064. doi: 10.3934/dcds.2016064 
[4] 
Bernd Kawohl, Vasilii Kurta. A Liouville comparison principle for solutions of singular quasilinear elliptic secondorder partial differential inequalities. Communications on Pure and Applied Analysis, 2011, 10 (6) : 17471762. doi: 10.3934/cpaa.2011.10.1747 
[5] 
Rui Li, Yingjing Shi. Finitetime optimal consensus control for secondorder multiagent systems. Journal of Industrial and Management Optimization, 2014, 10 (3) : 929943. doi: 10.3934/jimo.2014.10.929 
[6] 
Hongwei Lou, Jiongmin Yong. Secondorder necessary conditions for optimal control of semilinear elliptic equations with leading term containing controls. Mathematical Control and Related Fields, 2018, 8 (1) : 5788. doi: 10.3934/mcrf.2018003 
[7] 
Hongwei Lou. Secondorder necessary/sufficient conditions for optimal control problems in the absence of linear structure. Discrete and Continuous Dynamical Systems  B, 2010, 14 (4) : 14451464. doi: 10.3934/dcdsb.2010.14.1445 
[8] 
Leonardo Colombo. Secondorder constrained variational problems on Lie algebroids: Applications to Optimal Control. Journal of Geometric Mechanics, 2017, 9 (1) : 145. doi: 10.3934/jgm.2017001 
[9] 
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 
[10] 
Gábor Kiss, Bernd Krauskopf. Stability implications of delay distribution for firstorder and secondorder systems. Discrete and Continuous Dynamical Systems  B, 2010, 13 (2) : 327345. doi: 10.3934/dcdsb.2010.13.327 
[11] 
Nguyen Thi Hoai. Asymptotic approximation to a solution of a singularly perturbed linearquadratic optimal control problem with secondorder linear ordinary differential equation of state variable. Numerical Algebra, Control and Optimization, 2021, 11 (4) : 495512. doi: 10.3934/naco.2020040 
[12] 
Shasha Hu, Yihong Xu, Yuhan Zhang. SecondOrder characterizations for setvalued equilibrium problems with variable ordering structures. Journal of Industrial and Management Optimization, 2022, 18 (1) : 469486. doi: 10.3934/jimo.2020164 
[13] 
Qilin Wang, Shengji Li, Kok Lay Teo. Continuity of secondorder adjacent derivatives for weak perturbation maps in vector optimization. Numerical Algebra, Control and Optimization, 2011, 1 (3) : 417433. doi: 10.3934/naco.2011.1.417 
[14] 
Qiong Meng, X. H. Tang. Multiple solutions of secondorder ordinary differential equation via Morse theory. Communications on Pure and Applied Analysis, 2012, 11 (3) : 945958. doi: 10.3934/cpaa.2012.11.945 
[15] 
KyeongHun Kim, Kijung Lee. A weighted $L_p$theory for secondorder parabolic and elliptic partial differential systems on a half space. Communications on Pure and Applied Analysis, 2016, 15 (3) : 761794. doi: 10.3934/cpaa.2016.15.761 
[16] 
José F. Cariñena, Javier de Lucas Araujo. Superposition rules and secondorder Riccati equations. Journal of Geometric Mechanics, 2011, 3 (1) : 122. doi: 10.3934/jgm.2011.3.1 
[17] 
Eugenii Shustin, Emilia Fridman, Leonid Fridman. Oscillations in a secondorder discontinuous system with delay. Discrete and Continuous Dynamical Systems, 2003, 9 (2) : 339358. doi: 10.3934/dcds.2003.9.339 
[18] 
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 
[19] 
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 
[20] 
Lucas Bonifacius, Ira Neitzel. Second order optimality conditions for optimal control of quasilinear parabolic equations. Mathematical Control and Related Fields, 2018, 8 (1) : 134. doi: 10.3934/mcrf.2018001 
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