A Separation Principle on Lie Groups

Details A Separation Principle on Lie Groups A Separation Principle on Lie Groups

2010-10-28

arxiv.org/abs/1010.6007v1

Mathematics

Optimization and Control

Submitted to IFAC 2011

Scientific paper

For linear time-invariant systems, a separation principle holds: stable observer and stable state feedback can be designed for the time-invariant system, and the combined observer and feedback will be stable. For non-linear systems, a local separation principle holds around steady-states, as the linearized system is time-invariant. This paper addresses the issue of a non-linear separation principle on Lie groups. For invariant systems on Lie groups, we prove there exists a large set of (time-varying) trajectories around which the linearized observer-controler system is time-invariant, as soon as a symmetry-preserving observer is used. Thus a separation principle holds around those trajectories. The theory is illustrated by a mobile robot example, and the developed ideas are then extended to a class of Lagrangian mechanical systems on Lie groups described by Euler-Poincare equations.

Affiliated with

Also associated with

No associations

Rating

A Separation Principle on Lie Groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Separation Principle on Lie Groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Separation Principle on Lie Groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-584153