Volume 27, 2021
|Number of page(s)||34|
|Published online||15 October 2021|
A minimal time optimal control for a drone landing problem
Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci,
* Corresponding author: firstname.lastname@example.org
Accepted: 25 September 2021
We study a variant of the classical safe landing optimal control problem in aerospace engineering, introduced by Miele (1962), where the target was to land a spacecraft on the moon by minimizing the consumption of fuel. A more modern model consists in replacing the spacecraft by a hybrid gas-electric drone. Assuming that the drone has a failure and that the thrust (representing the control) can act in both vertical directions, the new target is to land safely by minimizing time, no matter of what the consumption is. In dependence of the initial data (height, velocity, and fuel), we prove that the optimal control can be of four different kinds, all being piecewise constant. Our analysis covers all possible situations, including the nonexistence of a safe landing strategy due to the lack of fuel or for heights/velocities for which also a total braking is insufficient to stop the drone.
Mathematics Subject Classification: 34H10 / 49J15 / 49K15
Key words: Optimal control / minimum time / drone
© The authors. Published by EDP Sciences, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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