Lie Groups and Lie Algebra for Nonlinear System Dynamics

lie-algebraslie-groupsnonlinear systemreference-request

I have a background in machine learning and control theory. Lately, I shifted my focus towards nonlinear systems. I am interested in rigorous mathematical analysis, stability, and control of nonlinear dynamical systems.

I have a solid mathematical background in measure theory, functional analysis, and ergodic theory.

To be more specific, I am looking for some reference that:

  1. Introduces Lie Groups and Lie Algebra.

  2. Gives a special treatment for their applications in nonlinear systems.

I am citing the following article as a motivation

$[1]$ Chein-Shan Liu,
A Lie-group DSO(n) method for nonlinear dynamical systems,
Applied Mathematics Letters,
Volume 26, Issue 7,
2013,
Pages 710-717,
ISSN 0893-9659,
https://doi.org/10.1016/j.aml.2013.01.012.
(https://www.sciencedirect.com/science/article/pii/S0893965913000530)

Best Answer

If you're interested in control aspects of nonlinear systems you could have a look into the second edition of Sontag's "Mathematical Control Theory" (1998): in Chapter 4 Sontag treats non-linear control systems and how to study them via Lie theory.

Admittedly, this book is not an introduction to Lie groups & Lie algebras but I think it very much satisfies your second criterion which is why I felt inclined to mention it here.

Related Question