A Local Solution to the Output Regulation Problem for Sampled-Data Systems on Commutative Matrix Lie Groups

Abstract

We present a smooth nonlinear control law for a kinematic plant on commutative matrix Lie groups that achieves regulation, if the state tracking and estimation errors are initialized in a suitable neighbourhood of identity. We show that in exponential coordinates, the closed-loop dynamics are linear. Our control law uses output feedback; to this end, we propose an almost-globally defined state estimator.