Research article
Special Issues
The moon lander optimal control problem revisited

Dipartimento di Matematica, Politecnico di Milano, Piazza L. da Vinci, 32  20133 Milano, Italy

Received:
16 June 2020
Accepted:
09 September 2020
Published:
13 October 2020




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 bangbang 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): 114. doi: 10.3934/mine.2021040

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 bangbang and our results give a full characterization of the switch position.
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