The computation of Lie derivatives and Lie brackets based on automatic differentiation

摘要

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. (C) 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. [References: 43]