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.
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This work was partially supported by the National Science Foundation through the grant DMS 09-08204.
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Kawski, M. (2014). Lie Algebraic Methods in Nonlinear Control. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_79-1
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DOI: https://doi.org/10.1007/978-1-4471-5102-9_79-1
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