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A geometric analysis of trajectory design for underwater vehicles
1. | University of Hawaii, Department of Mathematics, Honolulu, HI 96822, United States, United States |
2. | Université d'Orléans, Laboratoire MAPMO, 45067 Orléans Cedex, France |
3. | University of Hawaii, Ocean & Resources Engineering Department, Honolulu, HI 96822, United States |
[1] |
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 |
[2] |
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 |
[3] |
Changzhi Wu, Kok Lay Teo, Volker Rehbock. Optimal control of piecewise affine systems with piecewise affine state feedback. Journal of Industrial and Management Optimization, 2009, 5 (4) : 737-747. doi: 10.3934/jimo.2009.5.737 |
[4] |
Larisa Manita, Mariya Ronzhina. Optimal spiral-like solutions near a singular extremal in a two-input control problem. Discrete and Continuous Dynamical Systems - B, 2022, 27 (6) : 3325-3343. doi: 10.3934/dcdsb.2021187 |
[5] |
Bosheng Chen, Huilai Li, Changchun Liu. Optimal distributed control for a coupled phase-field system. Discrete and Continuous Dynamical Systems - B, 2022, 27 (3) : 1789-1825. doi: 10.3934/dcdsb.2021110 |
[6] |
B. Bonnard, J.-B. Caillau, E. Trélat. Geometric optimal control of elliptic Keplerian orbits. Discrete and Continuous Dynamical Systems - B, 2005, 5 (4) : 929-956. doi: 10.3934/dcdsb.2005.5.929 |
[7] |
Qingkai Kong, Zhipeng Qiu, Zi Sang, Yun Zou. Optimal control of a vector-host epidemics model. Mathematical Control and Related Fields, 2011, 1 (4) : 493-508. doi: 10.3934/mcrf.2011.1.493 |
[8] |
Canghua Jiang, Kok Lay Teo, Ryan Loxton, Guang-Ren Duan. A neighboring extremal solution for an optimal switched impulsive control problem. Journal of Industrial and Management Optimization, 2012, 8 (3) : 591-609. doi: 10.3934/jimo.2012.8.591 |
[9] |
Anthony M. Bloch, Rohit Gupta, Ilya V. Kolmanovsky. Neighboring extremal optimal control for mechanical systems on Riemannian manifolds. Journal of Geometric Mechanics, 2016, 8 (3) : 257-272. doi: 10.3934/jgm.2016007 |
[10] |
Chongyang Liu, Wenjuan Sun, Xiaopeng Yi. Optimal control of a fractional smoking system. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2022071 |
[11] |
M. Delgado-Téllez, Alberto Ibort. On the geometry and topology of singular optimal control problems and their solutions. Conference Publications, 2003, 2003 (Special) : 223-233. doi: 10.3934/proc.2003.2003.223 |
[12] |
Dingjun Yao, Rongming Wang, Lin Xu. Optimal asset control of a geometric Brownian motion with the transaction costs and bankruptcy permission. Journal of Industrial and Management Optimization, 2015, 11 (2) : 461-478. doi: 10.3934/jimo.2015.11.461 |
[13] |
Elie Assémat, Marc Lapert, Dominique Sugny, Steffen J. Glaser. On the application of geometric optimal control theory to Nuclear Magnetic Resonance. Mathematical Control and Related Fields, 2013, 3 (4) : 375-396. doi: 10.3934/mcrf.2013.3.375 |
[14] |
Monique Chyba, Geoff Patterson, Gautier Picot, Mikael Granvik, Robert Jedicke, Jeremie Vaubaillon. Designing rendezvous missions with mini-moons using geometric optimal control. Journal of Industrial and Management Optimization, 2014, 10 (2) : 477-501. doi: 10.3934/jimo.2014.10.477 |
[15] |
Yves Dumont, Frederic Chiroleu. Vector control for the Chikungunya disease. Mathematical Biosciences & Engineering, 2010, 7 (2) : 313-345. doi: 10.3934/mbe.2010.7.313 |
[16] |
Pierluigi Colli, Gianni Gilardi, Jürgen Sprekels. Distributed optimal control of a nonstandard nonlocal phase field system with double obstacle potential. Evolution Equations and Control Theory, 2017, 6 (1) : 35-58. doi: 10.3934/eect.2017003 |
[17] |
Heinz Schättler, Urszula Ledzewicz. Perturbation feedback control: A geometric interpretation. Numerical Algebra, Control and Optimization, 2012, 2 (3) : 631-654. doi: 10.3934/naco.2012.2.631 |
[18] |
Joaquim P. Mateus, Paulo Rebelo, Silvério Rosa, César M. Silva, Delfim F. M. Torres. Optimal control of non-autonomous SEIRS models with vaccination and treatment. Discrete and Continuous Dynamical Systems - S, 2018, 11 (6) : 1179-1199. doi: 10.3934/dcdss.2018067 |
[19] |
Kbenesh Blayneh, Yanzhao Cao, Hee-Dae Kwon. Optimal control of vector-borne diseases: Treatment and prevention. Discrete and Continuous Dynamical Systems - B, 2009, 11 (3) : 587-611. doi: 10.3934/dcdsb.2009.11.587 |
[20] |
David L. Russell. Control via decoupling of a class of second order linear hybrid systems. Discrete and Continuous Dynamical Systems - S, 2014, 7 (6) : 1321-1334. doi: 10.3934/dcdss.2014.7.1321 |
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