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)

Local synchronization of sampled-data systems on one-parameter Lie subgroups

McCarthy, P. J., & Nielsen, C. (2017). Local synchronization of sampled-data systems on one-parameter Lie subgroups. 2017 American Control Conference (ACC), 3914–3919. https://doi.org/10.23919/ACC.2017.7963554We present a distributed nonlinear control law for synchronization of identical agents on one-parameter Lie subgroups. If the agents are initialized sufficiently close to one another, then synchronization is achieved exponentially fast. The proof does not use Jacobian linearization, instead the local nature of our result stems from our use of exponential coordi nates on a matrix Lie group. We characterize all equilibria of the network and provide a characterization of deadbeat performance for a complete connectivity graph

Passivity-Based Control of Sampled-Data Systems on Lie Groups with Linear Outputs

The final publication is available at Elsevier via http://dx.doi.org/https://doi.org/10.1016/j.ifacol.2016.10.299. © 2016. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/We present a method of stabilizing a sampled-data system that evolves on a matrix Lie group using passivity. The continuous-time plant is assumed passive with known storage function, and its passivity is preserved under sampling by redefining the output of the discretized plant and keeping the storage function. We show that driftlessness is a necessary condition for a sampled-data system on a matrix Lie group to be zero-state observable. The closed-loop sampled-data system is stabilized by any strictly passive controller, and we present a synthesis procedure for a strictly positive real LTI controller. The closed-loop system is shown to be asymptotically stable. This stabilization method is applied to asymptotic tracking of piecewise constant references.This research is supported by the Natural Sciences and Engineering Research Council of Canada

Tracking on lie group for robot manipulators

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