A hopf-algebraic formula for compositions of noncommuting flows

Eric Gehrig, Matthias Kawski

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Scopus citations

Abstract

The Chen-Fliess series is known to be an exponential Lie series. Previously explicit formulas for the iterated integral coefficients were known only for its factorization into a directed infinite product of exponentials. This factorization uses Hall sets and the Zinbiel product. We use the underlying Hopf algebra structure to derive explicit formulas for the corresponding coefficients in the logarithm of the series. This allows one to express the series as a single exponential. This work is closely related to Fer and Magnus expansions, and has interpretations in terms of a continuous Campbell-Baker-Hausdorff formula. The result facilitates work in nonlinear control, numerical integration and various applications that involve compositions of noncommuting flows.

Original languageEnglish (US)
Title of host publicationProceedings of the 47th IEEE Conference on Decision and Control, CDC 2008
Pages1569-1574
Number of pages6
DOIs
StatePublished - Dec 1 2008
Event47th IEEE Conference on Decision and Control, CDC 2008 - Cancun, Mexico
Duration: Dec 9 2008Dec 11 2008

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other47th IEEE Conference on Decision and Control, CDC 2008
CountryMexico
CityCancun
Period12/9/0812/11/08

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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  • Cite this

    Gehrig, E., & Kawski, M. (2008). A hopf-algebraic formula for compositions of noncommuting flows. In Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008 (pp. 1569-1574). [4738914] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2008.4738914