Non-linear Symmetry-preserving Observer on Lie Groups

Details Non-linear Symmetry-preserving Observer on Lie Groups Non-linear Symmetry-preserving Observer on Lie Groups

2007-07-16

arxiv.org/abs/0707.2286v2

IEEE Trans. Automatic Control. Vol 54 (7) pp:1709 - 1713, 2009

Mathematics

Optimization and Control

12 pages. Submitted. Preliminary version publicated in french in the CIFA proceedings and IFAC08

Scientific paper

In this paper we give a geometrical framework for the design of observers on finite-dimensional Lie groups for systems which possess some specific symmetries. The design and the error (between true and estimated state) equation are explicit and intrinsic. We consider also a particular case: left-invariant systems on Lie groups with right equivariant output. The theory yields a class of observers such that error equation is autonomous. The observers converge locally around any trajectory, and the global behavior is independent from the trajectory, which reminds of the linear stationary case.

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