November  2005, 5(4): 929-956. doi: 10.3934/dcdsb.2005.5.929

Geometric optimal control of elliptic Keplerian orbits


Institut de Mathématiques, Université de Bourgogne, 21078 Dijon, France


ENSEEIHT-IRIT (UMR CNRS 5505), Institut National Polytechnique de Toulouse, 31071 Toulouse, France


Laboratoire d'Analyse Numérique et EDP, Université de Paris-Sud, 91405 Orsay, France

Received  November 2004 Revised  June 2005 Published  August 2005

This article deals with the transfer of a satellite between Keplerian orbits. We study the controllability properties of the system and make a preliminary analysis of the time optimal control using the maximum principle. Second order sufficient conditions are also given. Finally, the time optimal trajectory to transfer the system from an initial low orbit with large eccentricity to a terminal geostationary orbit is obtained numerically.
Citation: 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

Alex Bombrun, Jean-Baptiste Pomet. Asymptotic behavior of time optimal orbital transfer for low thrust 2-body control system. Conference Publications, 2007, 2007 (Special) : 122-129. doi: 10.3934/proc.2007.2007.122


Yunlong Huang, P. S. Krishnaprasad. Sub-Riemannian geometry and finite time thermodynamics Part 1: The stochastic oscillator. Discrete and Continuous Dynamical Systems - S, 2020, 13 (4) : 1243-1268. doi: 10.3934/dcdss.2020072


Lucas Dahinden, Álvaro del Pino. Introducing sub-Riemannian and sub-Finsler billiards. Discrete and Continuous Dynamical Systems, 2022, 42 (7) : 3187-3232. doi: 10.3934/dcds.2022014


Nicolas Dirr, Federica Dragoni, Max von Renesse. Evolution by mean curvature flow in sub-Riemannian geometries: A stochastic approach. Communications on Pure and Applied Analysis, 2010, 9 (2) : 307-326. doi: 10.3934/cpaa.2010.9.307


Erlend Grong, Alexander Vasil’ev. Sub-Riemannian and sub-Lorentzian geometry on $SU(1,1)$ and on its universal cover. Journal of Geometric Mechanics, 2011, 3 (2) : 225-260. doi: 10.3934/jgm.2011.3.225


Daniel Genin, Serge Tabachnikov. On configuration spaces of plane polygons, sub-Riemannian geometry and periodic orbits of outer billiards. Journal of Modern Dynamics, 2007, 1 (2) : 155-173. doi: 10.3934/jmd.2007.1.155


Stefan Sommer, Anne Marie Svane. Modelling anisotropic covariance using stochastic development and sub-Riemannian frame bundle geometry. Journal of Geometric Mechanics, 2017, 9 (3) : 391-410. doi: 10.3934/jgm.2017015


Paul W. Y. Lee, Chengbo Li, Igor Zelenko. Ricci curvature type lower bounds for sub-Riemannian structures on Sasakian manifolds. Discrete and Continuous Dynamical Systems, 2016, 36 (1) : 303-321. doi: 10.3934/dcds.2016.36.303


Beatrice Abbondanza, Stefano Biagi. Riesz-type representation formulas for subharmonic functions in sub-Riemannian settings. Communications on Pure and Applied Analysis, 2021, 20 (9) : 3161-3192. doi: 10.3934/cpaa.2021101


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


Ling Yun Wang, Wei Hua Gui, Kok Lay Teo, Ryan Loxton, Chun Hua Yang. Time delayed optimal control problems with multiple characteristic time points: Computation and industrial applications. Journal of Industrial and Management Optimization, 2009, 5 (4) : 705-718. doi: 10.3934/jimo.2009.5.705


Hongwei Lou, Junjie Wen, Yashan Xu. Time optimal control problems for some non-smooth systems. Mathematical Control and Related Fields, 2014, 4 (3) : 289-314. doi: 10.3934/mcrf.2014.4.289


Akram Kheirabadi, Asadollah Mahmoudzadeh Vaziri, Sohrab Effati. Linear optimal control of time delay systems via Hermite wavelet. Numerical Algebra, Control and Optimization, 2020, 10 (2) : 143-156. doi: 10.3934/naco.2019044


Zhaohua Gong, Chongyang Liu, Yujing Wang. Optimal control of switched systems with multiple time-delays and a cost on changing control. Journal of Industrial and Management Optimization, 2018, 14 (1) : 183-198. doi: 10.3934/jimo.2017042


Ying Wu, Zhaohui Yuan, Yanpeng Wu. Optimal tracking control for networked control systems with random time delays and packet dropouts. Journal of Industrial and Management Optimization, 2015, 11 (4) : 1343-1354. doi: 10.3934/jimo.2015.11.1343


Simona Fornaro, Stefano Lisini, Giuseppe Savaré, Giuseppe Toscani. Measure valued solutions of sub-linear diffusion equations with a drift term. Discrete and Continuous Dynamical Systems, 2012, 32 (5) : 1675-1707. doi: 10.3934/dcds.2012.32.1675


Changjun Yu, Shuxuan Su, Yanqin Bai. On the optimal control problems with characteristic time control constraints. Journal of Industrial and Management Optimization, 2022, 18 (2) : 1305-1320. doi: 10.3934/jimo.2021021


Rui Li, Yingjing Shi. Finite-time optimal consensus control for second-order multi-agent systems. Journal of Industrial and Management Optimization, 2014, 10 (3) : 929-943. doi: 10.3934/jimo.2014.10.929


Y. Gong, X. Xiang. A class of optimal control problems of systems governed by the first order linear dynamic equations on time scales. Journal of Industrial and Management Optimization, 2009, 5 (1) : 1-10. doi: 10.3934/jimo.2009.5.1


Yuefen Chen, Yuanguo Zhu. Indefinite LQ optimal control with process state inequality constraints for discrete-time uncertain systems. Journal of Industrial and Management Optimization, 2018, 14 (3) : 913-930. doi: 10.3934/jimo.2017082

2021 Impact Factor: 1.497


  • PDF downloads (83)
  • HTML views (0)
  • Cited by (24)

Other articles
by authors

[Back to Top]