Research article
Special Issues
The moon lander optimal control problem revisited
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Dipartimento di Matematica, Politecnico di Milano, Piazza L. da Vinci, 32 - 20133 Milano, Italy
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Received:
16 June 2020
Accepted:
09 September 2020
Published:
13 October 2020
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We revisit the control problem for a spacecraft to land on the moon surface at rest with minimal fuel consumption. We show that a detailed analysis in the related 3D phase space uncovers the existence of infinitely many safe landing curves, contrary to several former 2D descriptions that implicitly claim the existence of just one such curve. Our results lead to a deeper understanding of the dynamics and allows for a precise characterization of the optimal control. Such control is known to be bang-bang and our results give a full characterization of the switch position.
Citation: Filippo Gazzola, Elsa M. Marchini. The moon lander optimal control problem revisited[J]. Mathematics in Engineering, 2021, 3(5): 1-14. doi: 10.3934/mine.2021040
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Abstract
We revisit the control problem for a spacecraft to land on the moon surface at rest with minimal fuel consumption. We show that a detailed analysis in the related 3D phase space uncovers the existence of infinitely many safe landing curves, contrary to several former 2D descriptions that implicitly claim the existence of just one such curve. Our results lead to a deeper understanding of the dynamics and allows for a precise characterization of the optimal control. Such control is known to be bang-bang and our results give a full characterization of the switch position.
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