Smooth approximations of single-input controlled Keplerian trajectories : homotopies and averaging: Proceedings of the CTS-HyCon Workshop on Nonlinear and Hybrid Control (10-12 Juillet 2006, Paris IV Sorbonne, France)

Bernard BONNARD; Jean-Baptiste CAILLAU; Romain Dujol

Smooth approximations of single-input controlled Keplerian trajectories : homotopies and averaging: Proceedings of the CTS-HyCon Workshop on Nonlinear and Hybrid Control (10-12 Juillet 2006, Paris IV Sorbonne, France)

Bernard BONNARD, Jean-Baptiste CAILLAU, Romain Dujol

Research output: Contribution in Book/Catalog/Report/Conference proceeding › Chapter

Abstract

This article deals with the optimal transfer of a satellite between Keplerian orbits when the control is oriented along the tangential direction. We consider the time-optimal control problem and the energy minimization problem. The optimal controls laws have discontinuities and continuations and averaging techniques are applied to smooth the discontinuities. The smooth approximations of the solutions are computed using a shooting method taking into account second-order optimality conditions.

Original language	English
Title of host publication	Taming Heterogeneity and Complexity of Embedded Control
Subtitle of host publication	Selected papers presented at the Joint CTS-HYCON Workshop on Nonlinear and Hybrid Control, Paris IV Sorbonne, 10-12 July 2006
Editors	Francoise LAMNABHI-LAGARRIGUE, Salah LAGHROUCHE, Antonio LORIA, Elena PANTELEY
Place of Publication	Londres
Publisher	International Scientific and Technical Encyclopaedia
Pages	73-96
Number of pages	24
Publication status	Published - 2006

Keywords

shooting method
continuation method
second-order optimality condition
single-input orbit transfer
averaging
Optimal control

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BONNARD, B., CAILLAU, J-B., & Dujol, R. (2006). Smooth approximations of single-input controlled Keplerian trajectories : homotopies and averaging: Proceedings of the CTS-HyCon Workshop on Nonlinear and Hybrid Control (10-12 Juillet 2006, Paris IV Sorbonne, France). In F. LAMNABHI-LAGARRIGUE, S. LAGHROUCHE, A. LORIA, & E. PANTELEY (Eds.), Taming Heterogeneity and Complexity of Embedded Control: Selected papers presented at the Joint CTS-HYCON Workshop on Nonlinear and Hybrid Control, Paris IV Sorbonne, 10-12 July 2006 (pp. 73-96). International Scientific and Technical Encyclopaedia. http://iste.co.uk/index.php?f=a&ACTION=View&id=171

BONNARD, Bernard ; CAILLAU, Jean-Baptiste ; Dujol, Romain. / Smooth approximations of single-input controlled Keplerian trajectories : homotopies and averaging : Proceedings of the CTS-HyCon Workshop on Nonlinear and Hybrid Control (10-12 Juillet 2006, Paris IV Sorbonne, France). Taming Heterogeneity and Complexity of Embedded Control: Selected papers presented at the Joint CTS-HYCON Workshop on Nonlinear and Hybrid Control, Paris IV Sorbonne, 10-12 July 2006. editor / Francoise LAMNABHI-LAGARRIGUE ; Salah LAGHROUCHE ; Antonio LORIA ; Elena PANTELEY. Londres : International Scientific and Technical Encyclopaedia, 2006. pp. 73-96

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abstract = "This article deals with the optimal transfer of a satellite between Keplerian orbits when the control is oriented along the tangential direction. We consider the time-optimal control problem and the energy minimization problem. The optimal controls laws have discontinuities and continuations and averaging techniques are applied to smooth the discontinuities. The smooth approximations of the solutions are computed using a shooting method taking into account second-order optimality conditions.",

keywords = " shooting method, continuation method, second-order optimality condition, single-input orbit transfer, averaging, Optimal control",

author = "Bernard BONNARD and Jean-Baptiste CAILLAU and Romain Dujol",

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BONNARD, B, CAILLAU, J-B & Dujol, R 2006, Smooth approximations of single-input controlled Keplerian trajectories : homotopies and averaging: Proceedings of the CTS-HyCon Workshop on Nonlinear and Hybrid Control (10-12 Juillet 2006, Paris IV Sorbonne, France). in F LAMNABHI-LAGARRIGUE, S LAGHROUCHE, A LORIA & E PANTELEY (eds), Taming Heterogeneity and Complexity of Embedded Control: Selected papers presented at the Joint CTS-HYCON Workshop on Nonlinear and Hybrid Control, Paris IV Sorbonne, 10-12 July 2006. International Scientific and Technical Encyclopaedia, Londres, pp. 73-96. <http://iste.co.uk/index.php?f=a&ACTION=View&id=171>

Smooth approximations of single-input controlled Keplerian trajectories : homotopies and averaging: Proceedings of the CTS-HyCon Workshop on Nonlinear and Hybrid Control (10-12 Juillet 2006, Paris IV Sorbonne, France). / BONNARD, Bernard; CAILLAU, Jean-Baptiste; Dujol, Romain.
Taming Heterogeneity and Complexity of Embedded Control: Selected papers presented at the Joint CTS-HYCON Workshop on Nonlinear and Hybrid Control, Paris IV Sorbonne, 10-12 July 2006. ed. / Francoise LAMNABHI-LAGARRIGUE; Salah LAGHROUCHE; Antonio LORIA; Elena PANTELEY. Londres: International Scientific and Technical Encyclopaedia, 2006. p. 73-96.

Research output: Contribution in Book/Catalog/Report/Conference proceeding › Chapter

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T2 - Proceedings of the CTS-HyCon Workshop on Nonlinear and Hybrid Control (10-12 Juillet 2006, Paris IV Sorbonne, France)

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AU - CAILLAU, Jean-Baptiste

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PY - 2006

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AB - This article deals with the optimal transfer of a satellite between Keplerian orbits when the control is oriented along the tangential direction. We consider the time-optimal control problem and the energy minimization problem. The optimal controls laws have discontinuities and continuations and averaging techniques are applied to smooth the discontinuities. The smooth approximations of the solutions are computed using a shooting method taking into account second-order optimality conditions.

KW - shooting method

KW - continuation method

KW - second-order optimality condition

KW - single-input orbit transfer

KW - averaging

KW - Optimal control

M3 - Chapter

SP - 73

EP - 96

BT - Taming Heterogeneity and Complexity of Embedded Control

A2 - LAMNABHI-LAGARRIGUE, Francoise

A2 - LAGHROUCHE, Salah

A2 - LORIA, Antonio

A2 - PANTELEY, Elena

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BONNARD B, CAILLAU J-B, Dujol R. Smooth approximations of single-input controlled Keplerian trajectories : homotopies and averaging: Proceedings of the CTS-HyCon Workshop on Nonlinear and Hybrid Control (10-12 Juillet 2006, Paris IV Sorbonne, France). In LAMNABHI-LAGARRIGUE F, LAGHROUCHE S, LORIA A, PANTELEY E, editors, Taming Heterogeneity and Complexity of Embedded Control: Selected papers presented at the Joint CTS-HYCON Workshop on Nonlinear and Hybrid Control, Paris IV Sorbonne, 10-12 July 2006. Londres: International Scientific and Technical Encyclopaedia. 2006. p. 73-96