A Brief Study of Property of Lie Bracket

Authors: Navneet Garg

DOI: https://doi.org/10.17605/OSF.IO/76RCT

Short DOI: https://doi.org/ggrs9g

Country: India

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Abstract: In this paper we propose a novel methodology for the analysis of autonomous vehicles seeking the extremum of an arbitrary smooth nonlinear map in the plane. By interpreting the extremum seeking schemes as input-affine systems with periodic excitations and by using the methodology of Lie brackets, we calculate a simplified system which approximates the qualitative behavior of the original one better than existing methods. Global representation and various properties of the rigid body attitude, i.e., SO(3), are investigated in this paper. The representations, Euler-Lagrange equation, and Hamilton's equation on the second bundle of SO(3) are formally given.

Keywords: Quaternions, Controllability, Space vehicles, Position measurement, Nonlinear equations, Optimal control, Control theory, Attitude control, Control systems, Aircraft.

Paper Id: 223

Published On: 2013-10-14

Published In: Volume 1, Issue 1, September-October 2013

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