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The computation of Lie derivatives and Lie brackets based on automatic differentiation
Author(s) -
Röbenack K.,
Reinschke K.J.
Publication year - 2004
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200320077
Subject(s) - computation , automatic differentiation , simple (philosophy) , symbolic computation , computer science , field (mathematics) , nonlinear system , algebra over a field , lie group , theoretical computer science , mathematics , algorithm , pure mathematics , physics , mathematical analysis , philosophy , epistemology , quantum mechanics
Many algorithms in the field of nonlinear control theory require Lie derivatives or Lie brackets. Up to now, the computation of these derivatives was practical only for simple systems or for systems with a special structure due to the amount of symbolical computations involved. The authors suggest a new approach which is based on automatic differentiation. This approach circumvents several disadvantages of symbolic computations. Moreover, the methods presented here are applicable not only to systems described by explicitly given mathematical expressions but also to systems given by algorithms using conventional programming languages or dedicated modelling languages, respectively.