The equivalence of controlled Lagrangian and controlled Hamiltonian systems

Dong Eui Chang, Anthony M. Bloch, Naomi E. Leonard, Jerrold E. Marsden, Craig A. Woolsey

Research output: Contribution to journalArticlepeer-review

122 Scopus citations


The purpose of this paper is to show that the method of controlled Lagrangians and its Hamiltonian counterpart (based on the notion of passivity) are equivalent under rather general hypotheses. We study the particular case of simple mechanical control systems (where the underlying Lagrangian is kinetic minus potential energy) subject to controls and external forces in some detail. The equivalence makes use of almost Poisson structures (Poisson brackets that may fail to satisfy the Jacobi identity) on the Hamiltonian side, which is the Hamiltonian counterpart of a class of gyroscopic forces on the Lagrangian side.

Original languageEnglish (US)
Pages (from-to)393-422
Number of pages30
JournalESAIM - Control, Optimisation and Calculus of Variations
StatePublished - Jun 2002
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Control and Optimization
  • Computational Mathematics


  • Controlled Hamiltonian
  • Controlled Lagrangian
  • Energy shaping
  • Equivalence
  • Lyapunov stability
  • Passivity


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