Implementation of efficient algorithms for globally optimal trajectories

L. C. Polymenakos, D. P. Bertsekas, J. N. Tsitsiklis

Research output: Contribution to journalArticlepeer-review

37 Scopus citations


We consider a continuous-space shortest path problem in a two-dimensional plane. This is the problem of finding a trajectory that starts at a given point, ends at the boundary of a compact set of ℜ2, and minimizes a cost function of the form ∫0T r(x(t)) dt + q(x(T)). For a discretized version of this problem, a Dijkstra-like method that requires one iteration per discretization point has been developed by Tsitsiklis [10]. Here we develop some new label correcting-like methods based on the Small Label First methods of Bertsekas [2] and Bertsekas et al. [6]. We prove the finite termination of these methods, and we present computational results showing that they are competitive and often superior to the Dijkstra-like method and are also much faster than the traditional Jacobi and Gauss-Seidel methods.

Original languageEnglish (US)
Pages (from-to)278-283
Number of pages6
JournalIEEE Transactions on Automatic Control
Issue number2
StatePublished - 1998
Externally publishedYes


  • Label correcting
  • Label setting
  • Optimal control
  • Shortest paths

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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