Minimum-Fuel / Fuel-Optimal

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

An optimal control strategy that maximizes the spacecraft's remaining mass after soft landing. The terminal performance index is taken as J=m(tf), i.e., maximizing terminal mass, which is equivalent to minimizing total fuel consumption. Unlike zero-fuel optimization, minimum-fuel optimization focuses on achieving the least fuel expenditure while satisfying terminal velocity and position constraints. By Pontryagin's maximum principle, the fuel-optimal control law takes the form of bang-bang engine control: when the switching function S(t) is positive, the engine operates at maximum thrust; when negative, it shuts off, producing a continuously braking optimal descent trajectory.

Application Value

In low-thrust trajectory optimization, this propulsion approach achieves low-energy transfers through sustained acceleration over long durations, offering superior fuel economy compared to high-thrust systems.

  • Lunar Fly-by Method
  • Reachability Set
  • Maximum-Energy Escape Trajectory
  • Laplace Method

References

  • Zhou Jingyang and Zhou Di - 2007 - Precise Modeling and Optimal Trajectory Design for Lunar Lander Soft Landing
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Contributors: ouyangjiahong, Ou Yang Jiahong