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The moon lander optimal control problem revisited

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

This contribution is part of the Special Issue: Partial Differential Equations from theory to applications—Dedicated to Alberto Farina, on the occasion of his 50th birthday
Guest Editors: Serena Dipierro; Luca Lombardini
Link: www.aimspress.com/mine/article/5752/special-articles

Special Issues: Partial Differential Equations from theory to applications—Dedicated to Alberto Farina, on the occasion of his 50th birthday

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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References

1. Evans LC, An Introduction to Mathematical Optimal Control Theory. Available from: https://math.berkeley.edu/evans/control.course.pdf.

2. Fattorini HO (1999) Infinite-Dimensional Optimization and Control Theory, Cambridge: Cambridge University Press.

3. Fleming W, Rishel R (1975) Deterministic and Stochastic Optimal Control, Springer.

4. Meditch JS (1964) On the problem of optimal thrust programming for a lunar soft kanding. IEEE T Automat Contr 9: 477–484.    

5. Miele A (1962) The calculus of variations in applied aerodynamics and flight mechanics, In: Optimization Techniques with Applications to Aerospace Systems, Academic Press, 99–170.

© 2021 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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