Optimal tracking and formation keeping near a general Keplerian orbit under nonlinear perturbations

Kwangwon Lee, Chandeok Park, Sang Young Park, Daniel J. Scheeres

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


This study presents a semi-analytic approach for optimal tracking and formation keeping with high precision. For a continuous-thrust propulsion system, optimal formation keeping problems near a general Keplerian orbit are formulated with respect to a reference trajectory which is an explicit function of time. A nonlinear optimal tracking control law is then derived in generic form as a function of the states by employing generating functions in the theory of Hamiltonian systems. The applicability of the overall process is not affected by the complexity of dynamics and the selection of coordinates. As it allows us to design a nonlinear optimal feedback controller in the Earth-centered inertial frame, a variety of nonlinear perturbations can be incorporated easily without complicated coordinate transformations. Numerical experiments demonstrate that the nonlinear tracking control logic achieves superior tracking accuracy and cost reduction by accommodating higher-order nonlinearities.

Original languageEnglish
Pages (from-to)1019-1028
Number of pages10
JournalAdvances in Space Research
Issue number6
Publication statusPublished - 2014 Sept 15

Bibliographical note

Funding Information:
This work was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning ( NRF-2012R1A1A1012351 ).

All Science Journal Classification (ASJC) codes

  • Aerospace Engineering
  • Astronomy and Astrophysics
  • Geophysics
  • Atmospheric Science
  • Space and Planetary Science
  • Earth and Planetary Sciences(all)


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