Homotopy method for minimum consumption orbit transfer problem
ESAIM: COCV, 12 2 (2006) 294-310
Published online: 2006-03-22
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
Minimum-Fuel Earth-Based Orbit Transfers Using Multiple-Domain Adaptive Radau Collocation
Brittanny V. Holden, Elisha R. Pager and Anil V. RaoJournal of Spacecraft and Rockets 62 (1) 257 (2025)
https://doi.org/10.2514/1.A35773
A Bilevel Optimal Control Method and Application to the Hybrid Electric Vehicle
Olivier Cots, Rémy Dutto, Sophie Jan and Serge LaporteOptimal Control Applications and Methods 46 (3) 1104 (2025)
https://doi.org/10.1002/oca.3247
Optimal control of a solar sail
Alesia Herasimenka, Lamberto Dell'Elce, Jean‐Baptiste Caillau and Jean‐Baptiste PometOptimal Control Applications and Methods 45 (6) 2837 (2024)
https://doi.org/10.1002/oca.3189
Minimum-fuel two-impulse transfer between coplanar noncoaxial elliptical orbits
Jing LiAdvances in Space Research 73 (1) 143 (2024)
https://doi.org/10.1016/j.asr.2023.10.008
Generic Homotopic Smoothing for Low-Thrust Optimal Control Problems With Power Constraints
Qian Xiao, Lincheng Li, Jingrui Zhang and Ming XuIEEE Transactions on Control Systems Technology 32 (4) 1487 (2024)
https://doi.org/10.1109/TCST.2024.3370908
Оптимизация траекторий с малой тягой в переменных Кустаанхеймо–Штифеля
К. Р. Корнеев and С. П. ТрофимовKosmičeskie issledovaniâ 62 (3) 264 (2024)
https://doi.org/10.31857/S0023420624030045
Solution space exploration of low-thrust minimum-time trajectory optimization by combining two homotopies
Jingrui Zhang, Qian Xiao and Lincheng LiAutomatica 148 110798 (2023)
https://doi.org/10.1016/j.automatica.2022.110798
Autonomous Guidance Between Quasiperiodic Orbits in Cislunar Space via Deep Reinforcement Learning
Lorenzo Federici, Andrea Scorsoglio, Alessandro Zavoli and Roberto FurfaroJournal of Spacecraft and Rockets 1 (2023)
https://doi.org/10.2514/1.A35747
Second-Order Conditions for Fuel-Optimal Control Problems with Variable Endpoints
Zheng ChenJournal of Guidance, Control, and Dynamics 45 (2) 335 (2022)
https://doi.org/10.2514/1.G005865
(2022)
https://doi.org/10.2514/6.2022-2274
(2022)
https://doi.org/10.2514/6.2022-2392
Satellite transfers between Keplerian orbits
Rui Dilão, Mariana Fernandes and Mariana SáCelestial Mechanics and Dynamical Astronomy 134 (5) (2022)
https://doi.org/10.1007/s10569-022-10102-7
Regular variables in the problem of low-thrust trajectory optimization
Kirill Romanovich Korneev and Sergey Pavlovich TrofimovKeldysh Institute Preprints (32) 1 (2022)
https://doi.org/10.20948/prepr-2022-32
Symplectic Pseudospectral Methods for Optimal Control
Xinwei Wang, Jie Liu and Haijun PengIntelligent Systems, Control and Automation: Science and Engineering, Symplectic Pseudospectral Methods for Optimal Control 97 15 (2021)
https://doi.org/10.1007/978-981-15-3438-6_3
Multi-Objective Optimization of Covariance and Energy for Asteroid Transfers
Erica L. Jenson and Daniel J. ScheeresJournal of Guidance, Control, and Dynamics 44 (7) 1253 (2021)
https://doi.org/10.2514/1.G005609
Practical Homotopy Methods for Finding the Best Minimum-Fuel Transfer in the Circular Restricted Three-Body Problem
Xun Pan and Binfeng PanIEEE Access 8 47845 (2020)
https://doi.org/10.1109/ACCESS.2020.2978246
Bounding Homotopy Method for Minimum-Time Low-Thrust Transfer in the Circular Restricted Three-Body Problem
Xun Pan, Binfeng Pan and Zenghao LiThe Journal of the Astronautical Sciences 67 (4) 1220 (2020)
https://doi.org/10.1007/s40295-020-00213-4
Newton-Kantorovich/Radau pseudospectral solution to rigid spacecraft time-optimal three-axis reorientation
Jing Lan and Jing LiAdvances in Space Research 65 (11) 2662 (2020)
https://doi.org/10.1016/j.asr.2020.02.023
Existence Domain for Solutions of Optimal Control Problems for Bounded-Thrust Spacecrafts
A. V. IvanyukhinJournal of Mathematical Sciences 239 (6) 817 (2019)
https://doi.org/10.1007/s10958-019-04328-4
A new fractional homotopy method for solving nonlinear optimal control problems
Binfeng Pan, Yangyang Ma and Yang NiActa Astronautica 161 12 (2019)
https://doi.org/10.1016/j.actaastro.2019.05.005
A quadratic homotopy method for fuel-optimal low-thrust trajectory design
Binfeng Pan, Xun Pan and Yangyang MaProceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 233 (5) 1741 (2019)
https://doi.org/10.1177/0954410018761965
Combination of Direct Methods and Homotopy in Numerical Optimal Control: Application to the Optimization of Chemotherapy in Cancer
Antoine Olivier and Camille PoucholJournal of Optimization Theory and Applications 181 (2) 479 (2019)
https://doi.org/10.1007/s10957-018-01461-z
Low-Thrust Minimum-Fuel Trajectory Optimization Using Multiple Shooting Augmented by Analytical Derivatives
Yazhe Meng, Hao Zhang and Yang GaoJournal of Guidance, Control, and Dynamics 42 (3) 662 (2019)
https://doi.org/10.2514/1.G003473
Launcher Performance with Reserves
Max CerfJournal of Spacecraft and Rockets 55 (6) 1559 (2018)
https://doi.org/10.2514/1.A34229
A robust homotopic approach for continuous variable low-thrust trajectory optimization
Mohammadreza Saghamanesh and Hexi BaoyinAdvances in Space Research 62 (11) 3095 (2018)
https://doi.org/10.1016/j.asr.2018.08.046
A new probability-one homotopy method for solving minimum-time low-thrust orbital transfer problems
Binfeng Pan, Xun Pan and Siqi ZhangAstrophysics and Space Science 363 (9) (2018)
https://doi.org/10.1007/s10509-018-3420-0
Transfer Between Invariant Manifolds: From Impulse Transfer to Low-Thrust Transfer
Maxime Chupin, Thomas Haberkorn and Emmanuel TrélatJournal of Guidance, Control, and Dynamics 41 (3) 658 (2018)
https://doi.org/10.2514/1.G002922
Neighboring optimal control for open-time multiburn orbital transfers
Zheng Chen and Shuo TangAerospace Science and Technology 74 37 (2018)
https://doi.org/10.1016/j.ast.2018.01.003
Geometric optimal control and applications to aerospace
Jiamin Zhu, Emmanuel Trélat and Max CerfPacific Journal of Mathematics for Industry 9 (1) (2017)
https://doi.org/10.1186/s40736-017-0033-4
Neighboring optimal control for fixed-time multi-burn orbital transfers
Zheng ChenAerospace Science and Technology 61 57 (2017)
https://doi.org/10.1016/j.ast.2016.11.021
Low-thrust Lyapunov to Lyapunov and Halo to Halo missions with L2-minimization
Maxime Chupin, Thomas Haberkorn and Emmanuel TrélatESAIM: Mathematical Modelling and Numerical Analysis 51 (3) 965 (2017)
https://doi.org/10.1051/m2an/2016044
Geometric and numerical methods for a state constrained minimum time control problem of an electric vehicle
Olivier CotsESAIM: Control, Optimisation and Calculus of Variations 23 (4) 1715 (2017)
https://doi.org/10.1051/cocv/2016070
Fuel-optimal low-thrust formation reconfiguration via Radau pseudospectral method
Jing LiAdvances in Space Research 58 (1) 1 (2016)
https://doi.org/10.1016/j.asr.2016.04.005
$\mathrm{L^1}$-Minimization for Mechanical Systems
Z. Chen, J.-B. Caillau and Y. ChitourSIAM Journal on Control and Optimization 54 (3) 1245 (2016)
https://doi.org/10.1137/15M1013274
Time-optimal three-axis reorientation of asymmetric rigid spacecraft via homotopic approach
Jing LiAdvances in Space Research 57 (10) 2204 (2016)
https://doi.org/10.1016/j.asr.2016.02.016
Optimality Conditions Applied to Free-Time Multiburn Optimal Orbital Transfers
Zheng ChenJournal of Guidance, Control, and Dynamics 39 (11) 2512 (2016)
https://doi.org/10.2514/1.G000284
$$\mathrm{L}^1$$ L 1 -optimality conditions for the circular restricted three-body problem
Zheng ChenCelestial Mechanics and Dynamical Astronomy 126 (4) 461 (2016)
https://doi.org/10.1007/s10569-016-9703-2
Double-Homotopy Method for Solving Optimal Control Problems
Binfeng Pan, Ping Lu, Xun Pan and Yangyang MaJournal of Guidance, Control, and Dynamics 39 (8) 1706 (2016)
https://doi.org/10.2514/1.G001553
Recent Advances in Celestial and Space Mechanics
Monique Chyba, Geoff Patterson and Gautier PicotMathematics for Industry, Recent Advances in Celestial and Space Mechanics 23 179 (2016)
https://doi.org/10.1007/978-3-319-27464-5_6
Time-optimal reorientation of the rigid spacecraft using a pseudospectral method integrated homotopic approach
Jing Li and Xiao-ning XiOptimal Control Applications and Methods 36 (6) 889 (2015)
https://doi.org/10.1002/oca.2145
Designing rendezvous missions with mini-moons using geometric optimal control
Monique Chyba, Geoff Patterson, Gautier Picot, et al.Journal of Industrial & Management Optimization 10 (2) 477 (2014)
https://doi.org/10.3934/jimo.2014.10.477
A COMBINED ADAPTIVE CONTROL PARAMETRIZATION AND HOMOTOPY CONTINUATION TECHNIQUE FOR THE NUMERICAL SOLUTION OF BANG–BANG OPTIMAL CONTROL PROBLEMS
M. A. MEHRPOUYA, M. SHAMSI and M. RAZZAGHIThe ANZIAM Journal 56 (1) 48 (2014)
https://doi.org/10.1017/S1446181114000261
Optimal On–Off Cooperative Maneuvers for Long-Term Satellite Cluster Flight
Leonel Mazal, Giorgio Mingotti and Pini GurfilJournal of Guidance, Control, and Dynamics 37 (2) 391 (2014)
https://doi.org/10.2514/1.61431
73 (2013)
https://doi.org/10.1002/9780470612217.ch6
A Hamiltonian approach to compute an energy efficient trajectory for a servomotor system
Yebin Wang, Koichiro Ueda and Scott A. BortoffAutomatica 49 (12) 3550 (2013)
https://doi.org/10.1016/j.automatica.2013.09.019
Minimum fuel control of the planar circular restricted three-body problem
J.-B. Caillau, B. Daoud and J. GergaudCelestial Mechanics and Dynamical Astronomy 114 (1-2) 137 (2012)
https://doi.org/10.1007/s10569-012-9443-x
Optimal Control and Applications to Aerospace: Some Results and Challenges
E. TrélatJournal of Optimization Theory and Applications 154 (3) 713 (2012)
https://doi.org/10.1007/s10957-012-0050-5
Differential continuation for regular optimal control problems
J.-B. Caillau, O. Cots and J. GergaudOptimization Methods and Software 27 (2) 177 (2012)
https://doi.org/10.1080/10556788.2011.593625
Shooting and numerical continuation methods for computing time-minimal and energy-minimal trajectories in the Earth-Moon system using low propulsion
Gautier PicotDiscrete & Continuous Dynamical Systems - B 17 (1) 245 (2012)
https://doi.org/10.3934/dcdsb.2012.17.245
(2012)
https://doi.org/10.2514/6.2012-4742
Fuel-Optimal Low-Thrust Reconfiguration of Formation- Flying Satellites via Homotopic Approach
Jing Li and Xiao-ning XiJournal of Guidance, Control, and Dynamics 35 (6) 1709 (2012)
https://doi.org/10.2514/1.57354
Homotopic approach and pseudospectral method applied jointly to low thrust trajectory optimization
Tieding Guo, Fanghua Jiang and Junfeng LiActa Astronautica 71 38 (2012)
https://doi.org/10.1016/j.actaastro.2011.08.008
The smooth continuation method in optimal control with an application to quantum systems
Bernard Bonnard, Nataliya Shcherbakova and Dominique SugnyESAIM: Control, Optimisation and Calculus of Variations 17 (1) 267 (2011)
https://doi.org/10.1051/cocv/2010004
Convergence Results for Smooth Regularizations of Hybrid Nonlinear Optimal Control Problems
T. Haberkorn and E. TrélatSIAM Journal on Control and Optimization 49 (4) 1498 (2011)
https://doi.org/10.1137/100809209
Indirect Optimization for Finite-Thrust Time-Optimal Orbital Maneuver
Xincheng Yue, Ying Yang and Zhiyong GengJournal of Guidance, Control, and Dynamics 33 (2) 628 (2010)
https://doi.org/10.2514/1.44885
Homotopy Algorithm for Optimal Control Problems with a Second-order State Constraint
Audrey HermantApplied Mathematics and Optimization 61 (1) 85 (2010)
https://doi.org/10.1007/s00245-009-9076-y
Recent Advances in Optimization and its Applications in Engineering
J.-B. Caillau, B. Daoud and J. GergaudRecent Advances in Optimization and its Applications in Engineering 205 (2010)
https://doi.org/10.1007/978-3-642-12598-0_18
1457 (2009)
https://doi.org/10.1109/CDC.2009.5399622
Geometric Orbital Transfer Using Averaging Techniques
B. Bonnard and G. JaninJournal of Dynamical and Control Systems 14 (2) 145 (2008)
https://doi.org/10.1007/s10883-008-9040-1
Stability and sensitivity analysis for optimal control problems with a first-order state constraint and application to continuation methods
Joseph Frédéric Bonnans and Audrey HermantESAIM: Control, Optimisation and Calculus of Variations 14 (4) 825 (2008)
https://doi.org/10.1051/cocv:2008016
Riemannian metric of the averaged energy minimization problem in orbital transfer with low thrust
Bernard Bonnard and Jean-Baptiste CaillauAnnales de l'Institut Henri Poincare (C) Non Linear Analysis 24 (3) 395 (2007)
https://doi.org/10.1016/j.anihpc.2006.03.013
Using switching detection and variational equations for the shooting method
Pierre Martinon and Joseph GergaudOptimal Control Applications and Methods 28 (2) 95 (2007)
https://doi.org/10.1002/oca.794
Optimality results in orbit transfer
Bernard Bonnard and Jean-Baptiste CaillauComptes Rendus. Mathématique 345 (6) 319 (2007)
https://doi.org/10.1016/j.crma.2007.07.028
Systems, Control, Modeling and Optimization
B. Bonnard, J. -B. Caillau and R. DujolIFIP International Federation for Information Processing, Systems, Control, Modeling and Optimization 202 79 (2006)
https://doi.org/10.1007/0-387-33882-9_8