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Optimal Control for the Moon Lander: The Classical Problem and Variants

In: New Trends and Challenges in Optimization Theory Applied to Space Engineering

Author

Listed:
  • Filippo Gazzola

    (Dipartimento di Matematica, Politecnico di Milano)

  • Elsa M. Marchini

    (Dipartimento di Matematica, Politecnico di Milano)

Abstract

These notes concern a classical optimal control problem in aerospace engineering, how to land safely a spacecraft on the moon. Starting from an analysis of the original problem proposed by Miele (The calculus of variations in applied aerodynamics and flight mechanics, 1962), consisting in minimizing the consumption of fuel used for landing, we study a variant of the problem consisting in minimizing the landing time with a different thrust control. We prove that the optimal control (if it exists) is piecewise constant and provides the exact landing strategy, in dependence of the initial data (height, velocity, and fuel of the lander).

Suggested Citation

  • Filippo Gazzola & Elsa M. Marchini, 2025. "Optimal Control for the Moon Lander: The Classical Problem and Variants," Springer Optimization and Its Applications, in: Piermarco Cannarsa & Alessandra Celletti & Giorgio Fasano & Leonardo Mazzini & Mauro Pontani & Emman (ed.), New Trends and Challenges in Optimization Theory Applied to Space Engineering, pages 131-142, Springer.
    • Handle: RePEc:spr:spochp:978-3-031-81253-8_10
    DOI: 10.1007/978-3-031-81253-8_10
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