Attractive set of optimal feedback control for the hill three-body problem

Mai Bando, Daniel J. Scheeres

Research output: Chapter in Book/Report/Conference proceedingConference contribution


This paper investigates the combination of optimal feedback control with the dynamical structure of the three-body problem. The results provide new insights for the design of continuous low-thrust spacecraft trajectories. Specifically, we solve for the attracting set of an equilibrium point under optimal control with quadratic cost. The analysis reveals the relation between the attractive set and original dynamics. In particular, we find that the asymptotic form of the attractive set to an equilibrium point or a fixed point under optimal control is completely defined by its left unstable eigenvectors and a term inversely proportional to its unstable eigenvalue.

Original languageEnglish
Title of host publicationSpaceflight Mechanics 2016
EditorsMartin T. Ozimek, Renato Zanetti, Angela L. Bowes, Ryan P. Russell, Martin T. Ozimek
PublisherUnivelt Inc.
Number of pages18
ISBN (Print)9780877036333
Publication statusPublished - 2016
Event26th AAS/AIAA Space Flight Mechanics Meeting, 2016 - Napa, United States
Duration: Feb 14 2016Feb 18 2016

Publication series

NameAdvances in the Astronautical Sciences
ISSN (Print)0065-3438


Other26th AAS/AIAA Space Flight Mechanics Meeting, 2016
Country/TerritoryUnited States

All Science Journal Classification (ASJC) codes

  • Aerospace Engineering
  • Space and Planetary Science


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