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A sructure‐preserving numerical method for the dynamic optimization of flexible mechanical systems
Author(s) -
Schneider Simeon,
Betsch Peter
Publication year - 2018
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201800286
Subject(s) - noether's theorem , discretization , homogeneous space , optimal control , mechanical system , extension (predicate logic) , mathematics , path (computing) , momentum (technical analysis) , mathematical optimization , control theory (sociology) , mathematical analysis , computer science , control (management) , geometry , artificial intelligence , economics , programming language , finance
If an optimal control problem has symmetries, associated generalized momentum maps are preserved quantities along an optimal path, as can be seen by the extension of Noether's theorem to optimal control problems. These symmetries on the control level are inherited from the underlying mechanical system. The presented discretization method does respect the symmetries on both levels, the mechanical system and the optimal control problem, and preserves the generalized momentum mapping.