Robust control of the Hill's problem with drag

David J.N. Limebeer, Deon Sabatta

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


There are significant advantages associated with the analysis of satellite trajectory control problems in the Hill's analysis framework. As with the circular restricted three-body problem (CRTBP) equations, the Hill's equations support three-dimensional “halo” orbits that require station-keeping control. These orbits are typically in regions of space close to a libration point. In most cases these orbits are unstable, with drag effects introducing uncertain exogenous forces. A two-degree-of-freedom (Formula presented.) control strategy is used to maintain a pre-selected orbit and introduce a quantifiable robust stability margin. The control study presented is based on a time-periodic (Formula presented.) state feedback law, and a time-periodic feed-forward control that is based on a linearized drag model. The efficacy of these ideas is demonstrated by simulation.

Original languageEnglish
Pages (from-to)268-286
Number of pages19
JournalInternational Journal of Robust and Nonlinear Control
Issue number1
Publication statusPublished - 10 Jan 2021


  • Halo orbit
  • Halo orbit symmetries
  • Hill's problem
  • periodic Riccati equation
  • periodic robust control
  • two-degree-of-freedom controller

ASJC Scopus subject areas

  • Control and Systems Engineering
  • General Chemical Engineering
  • Biomedical Engineering
  • Aerospace Engineering
  • Mechanical Engineering
  • Industrial and Manufacturing Engineering
  • Electrical and Electronic Engineering


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