-
Previous Article
On an optimal control problem in laser cutting with mixed finite-/infinite-dimensional constraints
- JIMO Home
- This Issue
-
Next Article
A new parallel splitting descent method for structured variational inequalities
Designing rendezvous missions with mini-moons using geometric optimal control
1. | Department of Mathematics, University of Hawaii at Manoa, Honolulu, United States, United States, United States |
2. | Department of Physics, University of Helsinki, Helsinki, Finland |
3. | Institute for Astronomy, University of Hawaii at Manoa, Honolulu, United States |
4. | Institut de Mécanique Céleste et de Calcul des Éphémérides, Observatoire de Paris, Paris, France |
References:
[1] |
A. A. Agrachev and A. V. Sarychev, On abnormals extremals for Lagrange variational problems,, J. Math. Systems. Estim. Control, 8 (1998), 87.
|
[2] |
A. A. Agrachev and Y. L. Sachkov, Control Theory from the Geometric Viewpoint,, Encyclopaedia of Mathematical Sciences, (2004).
|
[3] |
E. L. Allgower and K. Georg, Numerical Continuation Methods. An Introduction,, Springer Series in Computational Mathematics, (1990).
doi: 10.1007/978-3-642-61257-2. |
[4] |
V. I. Arnol'd, Mathematical Methods of Classical Mechanics,, 2nd edition, (1989).
|
[5] |
J. T. Betts and S. O. Erb, Optimal low thrust trajectories to the moon,, SIAM J. Appl. Dyn. Syst., 2 (2003), 144.
doi: 10.1137/S1111111102409080. |
[6] |
E. Belbruno, Capture Dynamics and Chaotic Motion in Celestial Mechanics. With Applications to the Construction of Low Energy Transfers,, Princeton University Press, (2004).
|
[7] |
E. Belbruno, Fly me to the Moon. An Insider'S Guide to the New Science of Space Travel,, Princeton University Press, (2007).
|
[8] |
B. Bonnard, J.-B. Caillau and G. Picot, Geometric and numerical techniques in optimal control of the two and three-body problems,, Commun. Inf. Syst., 10 (2010), 239.
doi: 10.4310/CIS.2010.v10.n4.a5. |
[9] |
B. Bonnard, J.-B. Caillau and E. Télat, Geometric optimal control of elliptic Keplerian orbits,, Discrete Cont. Dyn. Syst. Ser. B, 5 (2005), 929.
doi: 10.3934/dcdsb.2005.5.929. |
[10] |
B. Bonnard, J.-B. Caillau and E. Trélat, Second order optimality conditions in the smooth case and applications in optimal control,, ESAIM Control Optim. and Calc. Var., 13 (2007), 207.
doi: 10.1051/cocv:2007012. |
[11] |
B. Bonnard and M. Chyba, Singular Trajectories and their Role in Control Theory,, Mathématiques & Applications (Berlin) [Mathematics & Applications], (2003).
|
[12] |
B. Bonnard, L. Faubourg and E. Trélat, Mécanique Céleste et Contrôle des Véhicules Spatiaux,, Mathématiques & Applications (Berlin) [Mathematics & Applications], 51 (2006).
|
[13] |
B. Bonnard and I. Kupka, Théorie des singularités de l'application entrée/sortie et optimalité des trajectoires singulières dans le problème du temps minimal,, (French) [Theory of the singularities of the input/output mapping and optimality of singular trajectories in the minimal-time problem], 5 (1998), 111.
doi: 10.1515/form.1993.5.111. |
[14] |
B. Bonnard, N. Shcherbakova and D. Sugny, The smooth continuation method in optimal control with an application to quantum systems,, ESAIM Control Optim. and Calc. Var., 17 (2011), 267.
doi: 10.1051/cocv/2010004. |
[15] |
E. Bryson, Jr. and Y. C. Ho, Applied Optimal Control. Optimization, Estimation and Control,, Revised printing, (1975).
|
[16] |
J.-B. Caillau, Contribution à l'Etude du Contrôle en Temps Minimal des Transferts Orbitaux,, Ph.D thesis, (2000). Google Scholar |
[17] |
M. Chyba, G. Picot, G. Patterson, R. Jedicke, M. Granvik and J. Vaubaillon, Time-minimal orbital transfers to temporarily-captured natural Earth satellites,, to appear in OCA5 - Advances in Optimization and Control with Applications, (2013). Google Scholar |
[18] |
J.-B. Caillau, O. Cots and J. Gergaud, Differential continuation for regular optimal control problems,, Optim. Methods Softw., 27 (2012), 177.
doi: 10.1080/10556788.2011.593625. |
[19] |
B. Daoud, Contribution au Contrôle Optimal du Problème Circulaire Restreint des Trois Corps,, Ph.D thesis, (2011). Google Scholar |
[20] |
J. Gergaud and T. Haberkorn, Homotopy method for minimum consumption orbit transfer problem,, ESAIM Control Optim. Calc. Var., 12 (2006), 294.
doi: 10.1051/cocv:2006003. |
[21] |
G. Gómez, W. S. Koon, M. W. Lo, J. E. Marsden, J. Masdemont and S. D. Ross, Invariants manifolds, the spatial three-body problem and space mission design,, in AAS/AIAA Astrodynamics Specialtists Conference, (2001). Google Scholar |
[22] |
G. Gómez, W. S. Koon, M. W. Lo, J. E. Marsden, J. Masdemont and S. D. Ross, Connecting orbits and invariant manifolds in the spatial three-body problem,, Nonlinearity, 17 (2004), 1571.
doi: 10.1088/0951-7715/17/5/002. |
[23] |
M. Granvik, J. Vaubaillon and R. Jedicke, The population of natural Earth satellites,, Icarus, 218 (2012), 262.
doi: 10.1016/j.icarus.2011.12.003. |
[24] |
V. Jurdjevic, Geometric Control Theory,, Cambridge Studies in Advanced Mathematics, (1997).
|
[25] |
J. Kawagachi, A. Fujiwara and T. K. Uesugi, The ion engine cruise operation and the Earth swingby of Hayabusa (MUSES-C),, in Proceddings of the 55th International Astronotical Congress, (2004). Google Scholar |
[26] |
T. Kubota, T. Hashimoto, J. Kawagachi, M. Uo and M. Shirakawa, Guidance and Navigation of Hayabusa spacecraft to asteroid exploration and sample return mission,, in Proceddings of SICE-ICASE, (2006), 2793.
doi: 10.1109/SICE.2006.314761. |
[27] |
D. Liberzon, Calculus of Variations and Optimal Control Theory. A Concise Introduction,, Princeton University Press, (2012).
|
[28] |
H. Mäurer, First and second order sufficient optimality conditions in mathematical programming and optimal control,, in Mathematical Programming at Oberwolfach (Proc. Conf., (1979), 163.
|
[29] |
A. Moore, Discrete Mechanics and Optimal Control for Space Trajectory Design,, Ph.D thesis, (2011).
|
[30] |
I. Newton, Principes Mathématiques de la Philosophie Naturelle. Tome I, II. (French) Traduction de la Marquise du Chastellet, Augmentée des Commentaires de Clairaut,, Librairie Scientifique et Technique Albert Blanchard, (1966).
|
[31] |
G. Picot, Shooting and numerical continuation method for computing time-minimal and energy-minimal trajectories in the Earth-Moon system using low propulsion,, Discrete Cont. Dyn. Syst. Ser. B, 17 (2012), 245.
doi: 10.3934/dcdsb.2012.17.245. |
[32] |
L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze and E. F. Mishchenko, The Mathematical Theory of Optimal Processes,, Interscience Publishers John Wiley & Sons, (1962).
|
[33] |
G. Racca, B. H. Foing and M. Coradini, SMART-1: The first time of Europe to the Moon,, Earth, 85-86 (2001), 85. Google Scholar |
[34] |
G. Racca et al., SMART-1 mission description and development status,, Planetary and Space Science, 50 (2002), 1323. Google Scholar |
[35] |
A. G. Santo, S. C Lee and R. E Gold, NEAR spacecraft and instrumentation,, J. Astronomical Sciences, 43 (1995), 373. Google Scholar |
[36] |
A. V. Sary\vchev, Index of second variation of a control system,, Mat. Sb. (N.S), 113(155) (1980), 464.
|
[37] |
V. Szebehely, Theory of Orbits: The Restricted Problem of Three Bodies,, Academic Press, (1967). Google Scholar |
[38] |
D. A Vallado, Fundamentals of Astrodynamics and Applications,, Springer, (2001). Google Scholar |
[39] |
V. Zeidan, First and second order sufficient conditions for optimal control and the calculus of variations,, Appl. Math. and Optim., 11 (1984), 209.
doi: 10.1007/BF01442179. |
show all references
References:
[1] |
A. A. Agrachev and A. V. Sarychev, On abnormals extremals for Lagrange variational problems,, J. Math. Systems. Estim. Control, 8 (1998), 87.
|
[2] |
A. A. Agrachev and Y. L. Sachkov, Control Theory from the Geometric Viewpoint,, Encyclopaedia of Mathematical Sciences, (2004).
|
[3] |
E. L. Allgower and K. Georg, Numerical Continuation Methods. An Introduction,, Springer Series in Computational Mathematics, (1990).
doi: 10.1007/978-3-642-61257-2. |
[4] |
V. I. Arnol'd, Mathematical Methods of Classical Mechanics,, 2nd edition, (1989).
|
[5] |
J. T. Betts and S. O. Erb, Optimal low thrust trajectories to the moon,, SIAM J. Appl. Dyn. Syst., 2 (2003), 144.
doi: 10.1137/S1111111102409080. |
[6] |
E. Belbruno, Capture Dynamics and Chaotic Motion in Celestial Mechanics. With Applications to the Construction of Low Energy Transfers,, Princeton University Press, (2004).
|
[7] |
E. Belbruno, Fly me to the Moon. An Insider'S Guide to the New Science of Space Travel,, Princeton University Press, (2007).
|
[8] |
B. Bonnard, J.-B. Caillau and G. Picot, Geometric and numerical techniques in optimal control of the two and three-body problems,, Commun. Inf. Syst., 10 (2010), 239.
doi: 10.4310/CIS.2010.v10.n4.a5. |
[9] |
B. Bonnard, J.-B. Caillau and E. Télat, Geometric optimal control of elliptic Keplerian orbits,, Discrete Cont. Dyn. Syst. Ser. B, 5 (2005), 929.
doi: 10.3934/dcdsb.2005.5.929. |
[10] |
B. Bonnard, J.-B. Caillau and E. Trélat, Second order optimality conditions in the smooth case and applications in optimal control,, ESAIM Control Optim. and Calc. Var., 13 (2007), 207.
doi: 10.1051/cocv:2007012. |
[11] |
B. Bonnard and M. Chyba, Singular Trajectories and their Role in Control Theory,, Mathématiques & Applications (Berlin) [Mathematics & Applications], (2003).
|
[12] |
B. Bonnard, L. Faubourg and E. Trélat, Mécanique Céleste et Contrôle des Véhicules Spatiaux,, Mathématiques & Applications (Berlin) [Mathematics & Applications], 51 (2006).
|
[13] |
B. Bonnard and I. Kupka, Théorie des singularités de l'application entrée/sortie et optimalité des trajectoires singulières dans le problème du temps minimal,, (French) [Theory of the singularities of the input/output mapping and optimality of singular trajectories in the minimal-time problem], 5 (1998), 111.
doi: 10.1515/form.1993.5.111. |
[14] |
B. Bonnard, N. Shcherbakova and D. Sugny, The smooth continuation method in optimal control with an application to quantum systems,, ESAIM Control Optim. and Calc. Var., 17 (2011), 267.
doi: 10.1051/cocv/2010004. |
[15] |
E. Bryson, Jr. and Y. C. Ho, Applied Optimal Control. Optimization, Estimation and Control,, Revised printing, (1975).
|
[16] |
J.-B. Caillau, Contribution à l'Etude du Contrôle en Temps Minimal des Transferts Orbitaux,, Ph.D thesis, (2000). Google Scholar |
[17] |
M. Chyba, G. Picot, G. Patterson, R. Jedicke, M. Granvik and J. Vaubaillon, Time-minimal orbital transfers to temporarily-captured natural Earth satellites,, to appear in OCA5 - Advances in Optimization and Control with Applications, (2013). Google Scholar |
[18] |
J.-B. Caillau, O. Cots and J. Gergaud, Differential continuation for regular optimal control problems,, Optim. Methods Softw., 27 (2012), 177.
doi: 10.1080/10556788.2011.593625. |
[19] |
B. Daoud, Contribution au Contrôle Optimal du Problème Circulaire Restreint des Trois Corps,, Ph.D thesis, (2011). Google Scholar |
[20] |
J. Gergaud and T. Haberkorn, Homotopy method for minimum consumption orbit transfer problem,, ESAIM Control Optim. Calc. Var., 12 (2006), 294.
doi: 10.1051/cocv:2006003. |
[21] |
G. Gómez, W. S. Koon, M. W. Lo, J. E. Marsden, J. Masdemont and S. D. Ross, Invariants manifolds, the spatial three-body problem and space mission design,, in AAS/AIAA Astrodynamics Specialtists Conference, (2001). Google Scholar |
[22] |
G. Gómez, W. S. Koon, M. W. Lo, J. E. Marsden, J. Masdemont and S. D. Ross, Connecting orbits and invariant manifolds in the spatial three-body problem,, Nonlinearity, 17 (2004), 1571.
doi: 10.1088/0951-7715/17/5/002. |
[23] |
M. Granvik, J. Vaubaillon and R. Jedicke, The population of natural Earth satellites,, Icarus, 218 (2012), 262.
doi: 10.1016/j.icarus.2011.12.003. |
[24] |
V. Jurdjevic, Geometric Control Theory,, Cambridge Studies in Advanced Mathematics, (1997).
|
[25] |
J. Kawagachi, A. Fujiwara and T. K. Uesugi, The ion engine cruise operation and the Earth swingby of Hayabusa (MUSES-C),, in Proceddings of the 55th International Astronotical Congress, (2004). Google Scholar |
[26] |
T. Kubota, T. Hashimoto, J. Kawagachi, M. Uo and M. Shirakawa, Guidance and Navigation of Hayabusa spacecraft to asteroid exploration and sample return mission,, in Proceddings of SICE-ICASE, (2006), 2793.
doi: 10.1109/SICE.2006.314761. |
[27] |
D. Liberzon, Calculus of Variations and Optimal Control Theory. A Concise Introduction,, Princeton University Press, (2012).
|
[28] |
H. Mäurer, First and second order sufficient optimality conditions in mathematical programming and optimal control,, in Mathematical Programming at Oberwolfach (Proc. Conf., (1979), 163.
|
[29] |
A. Moore, Discrete Mechanics and Optimal Control for Space Trajectory Design,, Ph.D thesis, (2011).
|
[30] |
I. Newton, Principes Mathématiques de la Philosophie Naturelle. Tome I, II. (French) Traduction de la Marquise du Chastellet, Augmentée des Commentaires de Clairaut,, Librairie Scientifique et Technique Albert Blanchard, (1966).
|
[31] |
G. Picot, Shooting and numerical continuation method for computing time-minimal and energy-minimal trajectories in the Earth-Moon system using low propulsion,, Discrete Cont. Dyn. Syst. Ser. B, 17 (2012), 245.
doi: 10.3934/dcdsb.2012.17.245. |
[32] |
L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze and E. F. Mishchenko, The Mathematical Theory of Optimal Processes,, Interscience Publishers John Wiley & Sons, (1962).
|
[33] |
G. Racca, B. H. Foing and M. Coradini, SMART-1: The first time of Europe to the Moon,, Earth, 85-86 (2001), 85. Google Scholar |
[34] |
G. Racca et al., SMART-1 mission description and development status,, Planetary and Space Science, 50 (2002), 1323. Google Scholar |
[35] |
A. G. Santo, S. C Lee and R. E Gold, NEAR spacecraft and instrumentation,, J. Astronomical Sciences, 43 (1995), 373. Google Scholar |
[36] |
A. V. Sary\vchev, Index of second variation of a control system,, Mat. Sb. (N.S), 113(155) (1980), 464.
|
[37] |
V. Szebehely, Theory of Orbits: The Restricted Problem of Three Bodies,, Academic Press, (1967). Google Scholar |
[38] |
D. A Vallado, Fundamentals of Astrodynamics and Applications,, Springer, (2001). Google Scholar |
[39] |
V. Zeidan, First and second order sufficient conditions for optimal control and the calculus of variations,, Appl. Math. and Optim., 11 (1984), 209.
doi: 10.1007/BF01442179. |
[1] |
Guillaume Bal, Wenjia Jing. Homogenization and corrector theory for linear transport in random media. Discrete & Continuous Dynamical Systems - A, 2010, 28 (4) : 1311-1343. doi: 10.3934/dcds.2010.28.1311 |
[2] |
W. Cary Huffman. On the theory of $\mathbb{F}_q$-linear $\mathbb{F}_{q^t}$-codes. Advances in Mathematics of Communications, 2013, 7 (3) : 349-378. doi: 10.3934/amc.2013.7.349 |
[3] |
Yila Bai, Haiqing Zhao, Xu Zhang, Enmin Feng, Zhijun Li. The model of heat transfer of the arctic snow-ice layer in summer and numerical simulation. Journal of Industrial & Management Optimization, 2005, 1 (3) : 405-414. doi: 10.3934/jimo.2005.1.405 |
[4] |
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 |
[5] |
J. Frédéric Bonnans, Justina Gianatti, Francisco J. Silva. On the convergence of the Sakawa-Shindo algorithm in stochastic control. Mathematical Control & Related Fields, 2016, 6 (3) : 391-406. doi: 10.3934/mcrf.2016008 |
[6] |
Diana Keller. Optimal control of a linear stochastic Schrödinger equation. Conference Publications, 2013, 2013 (special) : 437-446. doi: 10.3934/proc.2013.2013.437 |
[7] |
Alberto Bressan, Ke Han, Franco Rampazzo. On the control of non holonomic systems by active constraints. Discrete & Continuous Dynamical Systems - A, 2013, 33 (8) : 3329-3353. doi: 10.3934/dcds.2013.33.3329 |
[8] |
Paula A. González-Parra, Sunmi Lee, Leticia Velázquez, Carlos Castillo-Chavez. A note on the use of optimal control on a discrete time model of influenza dynamics. Mathematical Biosciences & Engineering, 2011, 8 (1) : 183-197. doi: 10.3934/mbe.2011.8.183 |
[9] |
Guirong Jiang, Qishao Lu. The dynamics of a Prey-Predator model with impulsive state feedback control. Discrete & Continuous Dynamical Systems - B, 2006, 6 (6) : 1301-1320. doi: 10.3934/dcdsb.2006.6.1301 |
[10] |
A. K. Misra, Anupama Sharma, Jia Li. A mathematical model for control of vector borne diseases through media campaigns. Discrete & Continuous Dynamical Systems - B, 2013, 18 (7) : 1909-1927. doi: 10.3934/dcdsb.2013.18.1909 |
[11] |
Luke Finlay, Vladimir Gaitsgory, Ivan Lebedev. Linear programming solutions of periodic optimization problems: approximation of the optimal control. Journal of Industrial & Management Optimization, 2007, 3 (2) : 399-413. doi: 10.3934/jimo.2007.3.399 |
[12] |
Shanjian Tang, Fu Zhang. Path-dependent optimal stochastic control and viscosity solution of associated Bellman equations. Discrete & Continuous Dynamical Systems - A, 2015, 35 (11) : 5521-5553. doi: 10.3934/dcds.2015.35.5521 |
[13] |
Peter Benner, Jens Saak, M. Monir Uddin. Balancing based model reduction for structured index-2 unstable descriptor systems with application to flow control. Numerical Algebra, Control & Optimization, 2016, 6 (1) : 1-20. doi: 10.3934/naco.2016.6.1 |
2019 Impact Factor: 1.366
Tools
Metrics
Other articles
by authors
[Back to Top]