Approximate Tracking for Systems on Three-dimensional Matrix Lie Groups via Feedback Nilpotentization

A wide range of dynamical systems from elds as diverse as mechanics, electrical networks and molecular chemistry can be modeled by invariant systems on matrix Lie groups. This paper extends the concept of approximate tracking in the high-frequency limit to non-nilpotent three-dimensional matrix Lie groups by making use of feedback nilpotentization for the local representations of these systems. Further it is shown how to convert these tracking controls involving a state-feedback to an open-loop control law, which can be interpreted as an approximate inverse of the original system.