Time optimal swing-up of the planar pendulum

Paolo Mason, Mireille Broucke, Benedetto Piccoli

Research output: Contribution to journalArticlepeer-review

46 Scopus citations


This paper presents qualitative results on the global structure of the time optimal trajectories of the planar pendulum on a cart. This mechanical system is a benchmark to test nonlinear control methods and various papers addressed the problem of computing time optimal open-loop controls. Relying on the theory of optimal synthesis, we provide a discontinuous feedback giving optimal solutions for any initial data. The approach is that of geometric control theory.

Original languageEnglish (US)
Pages (from-to)1876-1886
Number of pages11
JournalIEEE Transactions on Automatic Control
Issue number8
StatePublished - 2008
Externally publishedYes

All Science Journal Classification (ASJC) codes

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


  • Inverted pendulum
  • Stabilization
  • Time optimal control


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