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Matching and stabilization of discrete mechanical systems
Author(s) -
Bloch Anthony M.,
Leok Melvin,
Marsden Jerrold E.,
Zenkov Dmitry V.
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700390
Subject(s) - matching (statistics) , context (archaeology) , symmetry (geometry) , lagrangian , mechanical system , discrete symmetry , computer science , control theory (sociology) , discrete system , mathematics , statistical physics , classical mechanics , physics , algorithm , artificial intelligence , control (management) , geometry , homogeneous space , paleontology , statistics , biology
Controlled Lagrangian and matching techniques are developed for the stabilization of equilibria of discrete mechanical systems with symmetry as well as broken symmetry. Interesting new phenomena arise in the controlled Lagrangian approach in the discrete context that are not present in the continuous theory. Specifically, a nonconservative force that is necessary for matching in the discrete setting is introduced. The paper also discusses digital and model predictive controllers. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)