Controlled Lagrangians and the stabilization of Euler-Poincaré mechanical systems

Anthony M. Bloch, Naomi Ehrich Leonard, Jerrold E. Marsden

Research output: Contribution to journalArticle

37 Scopus citations

Abstract

In this paper we develop a constructive approach to the determination of stabilizing control laws for a class of Lagrangian mechanical systems with symmetry - systems whose underlying dynamics are governed by the Euler-Poincaré equations. This work extends our previous work on the stabilization of mechanical control systems using the method of controlled Lagrangians. The guiding principle behind our methodology is to develop a class of stabilizing feedback control laws which yield closed-loop dynamics that remain in Lagrangian form. Using the methodology for Euler-Poincaré systems, we analyse stabilization of a satellite and an underwater vehicle controlled with momentum wheels.

Original languageEnglish (US)
Pages (from-to)191-214
Number of pages24
JournalInternational Journal of Robust and Nonlinear Control
Volume11
Issue number3
DOIs
StatePublished - Mar 2001

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Chemical Engineering(all)
  • Biomedical Engineering
  • Aerospace Engineering
  • Mechanical Engineering
  • Industrial and Manufacturing Engineering
  • Electrical and Electronic Engineering

Keywords

  • Lagrangian systems
  • Nonlinear control
  • Stabilization
  • Symmetry

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