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

McCarthy, P. J., & Nielsen, C. (2018). A Local Solution to the Output Regulation Problem for Sampled-Data Systems on Commutative Matrix Lie Groups. 2018 Annual American Control Conference (ACC), 6055–6060. https://doi.org/10.23919/ACC.2018.8431108We 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.Funder 1, Supported by the Ontario Graduate Scholarship (OGS) || Funder 2, Supported by the Natural Sciences and Engineering Research Council of Canada (NSERC)