Encyclopedia of Systems and Control

2015 Edition
| Editors: John Baillieul, Tariq Samad

Lie Algebraic Methods in Nonlinear Control

Reference work entry
First Online:
DOI: https://doi.org/10.1007/978-1-4471-5058-9_79
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Abstract

Lie algebraic methods generalize matrix methods and algebraic rank conditions to smooth nonlinear systems. They capture the essence of noncommuting flows and give rise to noncommutative analogues of Taylor expansions. Lie algebraic rank conditions determine controllability, observability, and optimality. Lie algebraic methods are also employed for state-space realization, control design, and path planning.

Keywords

Baker-Campbell-Hausdorff formula Chen-Fliess series Lie bracket 
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Copyright information

© Springer-Verlag London 2015

Authors and Affiliations

  1. 1.School of Mathematical and Statistical SciencesArizona State UniversityTempeUSA