Least-squares solution of a class of optimal space guidance problems via theory of connections

Roberto Furfaro, Daniele Mortari

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


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 polynomial 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 polynomial expansion and ToC, we solve the TPBVP for a class of optimal guidance problems including energy-optimal constrained landing on planetary bodies and fixed-time optimal intercept for a target-interceptor scenario. An analysis of the performance in terms of accuracy and computational time is provided to evaluate the performance of the proposed algorithm for realtime implementation.

Original languageEnglish (US)
Title of host publicationAAS/AIAA Astrodynamics Specialist Conference, 2018
EditorsPuneet Singla, Ryan M. Weisman, Belinda G. Marchand, Brandon A. Jones
PublisherUnivelt Inc.
Number of pages17
ISBN (Print)9780877036579
StatePublished - 2018
EventAAS/AIAA Astrodynamics Specialist Conference, 2018 - Snowbird, United States
Duration: Aug 19 2018Aug 23 2018

Publication series

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


ConferenceAAS/AIAA Astrodynamics Specialist Conference, 2018
Country/TerritoryUnited States

ASJC Scopus subject areas

  • Aerospace Engineering
  • Space and Planetary Science


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