Least-squares solution of a class of optimal space guidance problems via Theory of Connections

Roberto Furfaro, Daniele Mortari

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


In this paper, we apply a newly developed method to solve boundary value problems for differential equations to solve optimal space guidance problems in a fast and accurate fashion. The method relies on the least-squares solution of differential equations via orthogonal polynomials expansion and constrained expression as derived via Theory of Connection (ToC). The application of the optimal control theory to derive the first order necessary conditions for optimality, yields a Two-Point Boundary Value Problem (TPBVP) that must be solved to find state and costate. Combining orthogonal polynomials expansion and ToC, we solve the TPBVP for a class of optimal guidance problems including energy-optimal landing on planetary bodies and fixed-time optimal intercept for a target-interceptor scenario. The performance analysis in terms of accuracy shows the potential of the proposed methodology as applied to optimal guidance problems.

Original languageEnglish (US)
Pages (from-to)92-103
Number of pages12
JournalActa Astronautica
StatePublished - Mar 2020


  • Optimal guidance
  • Planetary landing
  • Theory of Connections

ASJC Scopus subject areas

  • Aerospace Engineering


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