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On the geometry and topology of singular optimal control problems and their solutions
1. | Departmento de Matemáticas, Universidad Carlos III de Madrid, Leganés 28911, Madrid, Spain |
2. | Department de Matemáticas, Universidad Carlos III De Madrid, Avda. de la Universidad 30, Leganés 28911, Madrid, Spain |
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Shihchung Chiang. Numerical optimal unbounded control with a singular integro-differential equation as a constraint. Conference Publications, 2013, 2013 (special) : 129-137. doi: 10.3934/proc.2013.2013.129 |
[2] |
Claudio Marchi. On the convergence of singular perturbations of Hamilton-Jacobi equations. Communications on Pure and Applied Analysis, 2010, 9 (5) : 1363-1377. doi: 10.3934/cpaa.2010.9.1363 |
[3] |
Ogabi Chokri. On the $L^p-$ theory of Anisotropic singular perturbations of elliptic problems. Communications on Pure and Applied Analysis, 2016, 15 (4) : 1157-1178. doi: 10.3934/cpaa.2016.15.1157 |
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Mazyar Ghani Varzaneh, Sebastian Riedel. A dynamical theory for singular stochastic delay differential equations Ⅱ: nonlinear equations and invariant manifolds. Discrete and Continuous Dynamical Systems - B, 2021, 26 (8) : 4587-4612. doi: 10.3934/dcdsb.2020304 |
[5] |
Huaiyu Jian, Xiaolin Liu, Hongjie Ju. The regularity for a class of singular differential equations. Communications on Pure and Applied Analysis, 2013, 12 (3) : 1307-1319. doi: 10.3934/cpaa.2013.12.1307 |
[6] |
Christian Lax, Sebastian Walcher. Singular perturbations and scaling. Discrete and Continuous Dynamical Systems - B, 2020, 25 (1) : 1-29. doi: 10.3934/dcdsb.2019170 |
[7] |
Masaki Hibino. Gevrey asymptotic theory for singular first order linear partial differential equations of nilpotent type — Part I —. Communications on Pure and Applied Analysis, 2003, 2 (2) : 211-231. doi: 10.3934/cpaa.2003.2.211 |
[8] |
Mohammed Al Horani, Angelo Favini, Hiroki Tanabe. Singular integro-differential equations with applications. Evolution Equations and Control Theory, 2021 doi: 10.3934/eect.2021051 |
[9] |
Zvi Artstein. Invariance principle in the singular perturbations limit. Discrete and Continuous Dynamical Systems - B, 2019, 24 (8) : 3653-3666. doi: 10.3934/dcdsb.2018309 |
[10] |
Youri V. Egorov, Evariste Sanchez-Palencia. Remarks on certain singular perturbations with ill-posed limit in shell theory and elasticity. Discrete and Continuous Dynamical Systems, 2011, 31 (4) : 1293-1305. doi: 10.3934/dcds.2011.31.1293 |
[11] |
W. Wei, H. M. Yin. Global solvability for a singular nonlinear Maxwell's equations. Communications on Pure and Applied Analysis, 2005, 4 (2) : 431-444. doi: 10.3934/cpaa.2005.4.431 |
[12] |
Z. Foroozandeh, Maria do rosário de Pinho, M. Shamsi. On numerical methods for singular optimal control problems: An application to an AUV problem. Discrete and Continuous Dynamical Systems - B, 2019, 24 (5) : 2219-2235. doi: 10.3934/dcdsb.2019092 |
[13] |
Térence Bayen, Marc Mazade, Francis Mairet. Analysis of an optimal control problem connected to bioprocesses involving a saturated singular arc. Discrete and Continuous Dynamical Systems - B, 2015, 20 (1) : 39-58. doi: 10.3934/dcdsb.2015.20.39 |
[14] |
Pierluigi Colli, Gianni Gilardi, Gabriela Marinoschi, Elisabetta Rocca. Optimal control for a phase field system with a possibly singular potential. Mathematical Control and Related Fields, 2016, 6 (1) : 95-112. doi: 10.3934/mcrf.2016.6.95 |
[15] |
Pierluigi Colli, Gianni Gilardi, Gabriela Marinoschi, Elisabetta Rocca. Optimal control for a conserved phase field system with a possibly singular potential. Evolution Equations and Control Theory, 2018, 7 (1) : 95-116. doi: 10.3934/eect.2018006 |
[16] |
Manfred Deistler. Singular arma systems: A structure theory. Numerical Algebra, Control and Optimization, 2019, 9 (3) : 383-391. doi: 10.3934/naco.2019025 |
[17] |
Suqi Ma, Zhaosheng Feng, Qishao Lu. A two-parameter geometrical criteria for delay differential equations. Discrete and Continuous Dynamical Systems - B, 2008, 9 (2) : 397-413. doi: 10.3934/dcdsb.2008.9.397 |
[18] |
Senoussi Guesmia, Abdelmouhcene Sengouga. Some singular perturbations results for semilinear hyperbolic problems. Discrete and Continuous Dynamical Systems - S, 2012, 5 (3) : 567-580. doi: 10.3934/dcdss.2012.5.567 |
[19] |
Michel Chipot, Senoussi Guesmia. On the asymptotic behavior of elliptic, anisotropic singular perturbations problems. Communications on Pure and Applied Analysis, 2009, 8 (1) : 179-193. doi: 10.3934/cpaa.2009.8.179 |
[20] |
Chiara Zanini. Singular perturbations of finite dimensional gradient flows. Discrete and Continuous Dynamical Systems, 2007, 18 (4) : 657-675. doi: 10.3934/dcds.2007.18.657 |
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