Necessary conditions for singular arcs for general restricted multi-body problem

Chandeok Park; I. Michael Ross; Qi Gong; Hui Yan

doi:10.1109/CDC.2010.5717305

Necessary conditions for singular arcs for general restricted multi-body problem

Chandeok Park, I. Michael Ross, Qi Gong, Hui Yan

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

9 Citations (Scopus)

Abstract

We analyze the optimality of intermediate thrust arcs (singular arcs) of a rocket trajectory subject to multiple gravitational bodies in the restricted multi-body problem. We derive a series of necessary conditions for optimality including the generalized Legendre-Clebsch condition, and an explicit formula for the singular optimal control law. Our derivations become identical to Lawden's classical result if the equations of motion are reduced for a central gravity field. As a means to illustrate the practical nature of our results, we apply them to a Moon-Earth transfer problem and show that the extremal solution is bang-singular-bang.

Original language	English
Title of host publication	2010 49th IEEE Conference on Decision and Control, CDC 2010
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	5816-5821
Number of pages	6
ISBN (Print)	9781424477456
DOIs	https://doi.org/10.1109/CDC.2010.5717305
Publication status	Published - 2010
Event	49th IEEE Conference on Decision and Control, CDC 2010 - Atlanta, United States Duration: 2010 Dec 15 → 2010 Dec 17

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	49th IEEE Conference on Decision and Control, CDC 2010
Country/Territory	United States
City	Atlanta
Period	10/12/15 → 10/12/17

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Modelling and Simulation
Control and Optimization

Access to Document

10.1109/CDC.2010.5717305

Cite this

Park, C., Ross, I. M., Gong, Q., & Yan, H. (2010). Necessary conditions for singular arcs for general restricted multi-body problem. In 2010 49th IEEE Conference on Decision and Control, CDC 2010 (pp. 5816-5821). Article 5717305 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2010.5717305

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title = "Necessary conditions for singular arcs for general restricted multi-body problem",

abstract = "We analyze the optimality of intermediate thrust arcs (singular arcs) of a rocket trajectory subject to multiple gravitational bodies in the restricted multi-body problem. We derive a series of necessary conditions for optimality including the generalized Legendre-Clebsch condition, and an explicit formula for the singular optimal control law. Our derivations become identical to Lawden's classical result if the equations of motion are reduced for a central gravity field. As a means to illustrate the practical nature of our results, we apply them to a Moon-Earth transfer problem and show that the extremal solution is bang-singular-bang.",

author = "Chandeok Park and Ross, {I. Michael} and Qi Gong and Hui Yan",

year = "2010",

doi = "10.1109/CDC.2010.5717305",

language = "English",

isbn = "9781424477456",

series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "5816--5821",

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note = "49th IEEE Conference on Decision and Control, CDC 2010 ; Conference date: 15-12-2010 Through 17-12-2010",

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Park, C, Ross, IM, Gong, Q & Yan, H 2010, Necessary conditions for singular arcs for general restricted multi-body problem. in 2010 49th IEEE Conference on Decision and Control, CDC 2010., 5717305, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 5816-5821, 49th IEEE Conference on Decision and Control, CDC 2010, Atlanta, United States, 10/12/15. https://doi.org/10.1109/CDC.2010.5717305

Necessary conditions for singular arcs for general restricted multi-body problem. / Park, Chandeok; Ross, I. Michael; Gong, Qi et al.
2010 49th IEEE Conference on Decision and Control, CDC 2010. Institute of Electrical and Electronics Engineers Inc., 2010. p. 5816-5821 5717305 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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T1 - Necessary conditions for singular arcs for general restricted multi-body problem

AU - Park, Chandeok

AU - Ross, I. Michael

AU - Gong, Qi

AU - Yan, Hui

PY - 2010

Y1 - 2010

N2 - We analyze the optimality of intermediate thrust arcs (singular arcs) of a rocket trajectory subject to multiple gravitational bodies in the restricted multi-body problem. We derive a series of necessary conditions for optimality including the generalized Legendre-Clebsch condition, and an explicit formula for the singular optimal control law. Our derivations become identical to Lawden's classical result if the equations of motion are reduced for a central gravity field. As a means to illustrate the practical nature of our results, we apply them to a Moon-Earth transfer problem and show that the extremal solution is bang-singular-bang.

AB - We analyze the optimality of intermediate thrust arcs (singular arcs) of a rocket trajectory subject to multiple gravitational bodies in the restricted multi-body problem. We derive a series of necessary conditions for optimality including the generalized Legendre-Clebsch condition, and an explicit formula for the singular optimal control law. Our derivations become identical to Lawden's classical result if the equations of motion are reduced for a central gravity field. As a means to illustrate the practical nature of our results, we apply them to a Moon-Earth transfer problem and show that the extremal solution is bang-singular-bang.

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DO - 10.1109/CDC.2010.5717305

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SN - 9781424477456

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 5816

EP - 5821

BT - 2010 49th IEEE Conference on Decision and Control, CDC 2010

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 49th IEEE Conference on Decision and Control, CDC 2010

Y2 - 15 December 2010 through 17 December 2010

ER -

Necessary conditions for singular arcs for general restricted multi-body problem

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