Sufficient conditions for a path-connected set of local solutions to an optimal control problem

Andy Borum, Timothy Bretl

Research output: Contribution to journalArticlepeer-review

Abstract

Consider a fixed-endpoint, fixed time optimal control problem with state and input taking values in Euclidean space. We show that if the Hamiltonian function associated with this problem satisfies a scale invariance property, then the set of all local solutions to this problem-over all possible terminal state constraints-is path-connected. We also show that this result extends to problems with additional constraints such as a bound on total cost. Finally, we use this result to show that the set of all curves that can be realized by a planar elastica is path-connected, and we describe how this result can be applied to the problem of robotic manipulation for nonrigid objects.

Original languageEnglish (US)
Pages (from-to)976-999
Number of pages24
JournalSIAM Journal on Applied Mathematics
Volume76
Issue number3
DOIs
StatePublished - 2016

Keywords

  • Conjugate points
  • Optimal control
  • Path-connectedness
  • Scale invariance

ASJC Scopus subject areas

  • Applied Mathematics

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