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On computation of the logarithm of the Chen-Fliess series for nonlinear systems. (English) Zbl 1157.93410

Zinober, Alan (ed.) et al., Nonlinear and adaptive control. NCN4 2001, 31 papers from the 4th workshop on nonlinear control network, Univ. of Sheffield, GB, June 25–28, 2001. Berlin: Springer (ISBN 3-540-43240-X). Lect. Notes Control Inf. Sci. 281, 317-326 (2003).
Summary: We obtain expressions for the logarithm of the Chen-Fliess series for a nonlinear control system. This logarithm provides an alternative to Sussmann’s exponential product expansion of the Chen-Fliess series. We also formulate a rule for generating the coefficient of any Lie brackets in the logarithm expansion.
For the entire collection see [Zbl 0996.00057].

MSC:

93C10 Nonlinear systems in control theory
17B66 Lie algebras of vector fields and related (super) algebras
93B29 Differential-geometric methods in systems theory (MSC2000)
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