Controlled Lagrangians and the stabilization of mechanical systems II: Potential shaping

Anthony M. Bloch, Dong Eui Chang, Naomi Ehrich Leonard, Jerrold E. Marsden

Research output: Contribution to journalArticle

244 Scopus citations

Abstract

We extend the method of controlled Lagrangians (CL) to include potential shaping, which achieves complete state-space asymptotic stabilization of mechanical systems. The CL method deals with mechanical systems with symmetry and provides symmetry-preserving kinetic shaping and feedback-controlled dissipation for state-space stabilization in all but the symmetry variables. Potential shaping complements the kinetic shaping by breaking symmetry and stabilizing the remaining state variables. The approach also extends the method of controlled Lagrangians to include a class of mechanical systems without symmetry such as the inverted pendulum on a cart that travels along an incline.

Original languageEnglish (US)
Pages (from-to)1556-1571
Number of pages16
JournalIEEE Transactions on Automatic Control
Volume46
Issue number10
DOIs
StatePublished - Oct 2001

All Science Journal Classification (ASJC) codes

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

Keywords

  • Lyapunov methods
  • Mechanical systems
  • Non-linear control
  • Stabilization
  • Tracking

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