Global Sampled-Data Regulation of a Class of Fully Actuated Invariant Systems on Simply Connected Nilpotent Matrix Lie Groups
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Date
2021-02-09
Authors
McCarthy, Philip James
Nielsen, Christopher
Advisor
Journal Title
Journal ISSN
Volume Title
Publisher
IEEE
Abstract
We examine a regulator problem for a class of fully actuated continuous-time invariant systems on Lie groups, using a discrete-time controller with constant sampling period. We present a smooth discrete-time control law that achieves global regulation on simply connected nilpotent Lie groups. We first solve the problem when both the plant state and exosystem state are available for feedback, then in the case where the plant state and plant output are available for feedback. The class of plant outputs considered includes, for example, the quantity to be regulated. This class of output allows us to use the classical Luenberger observer to estimate the exosystem states. In the full-information case, the regulation quantity on the Lie algebra is shown to decay exponentially to zero, which implies that it tends asymptotically to the identity on the Lie group.
Description
Mccarthy, P. J., & Nielsen, C. (2021). Global Sampled-Data Regulation of a Class of Fully Actuated Invariant Systems on Simply Connected Nilpotent Matrix Lie Groups. IEEE Transactions on Automatic Control, 1–1. https://doi.org/10.1109/TAC.2021.3058053
Keywords
Regulators, Regulation, Algebra, Stability analysis, Asymptotic stability, Trajectory, Mathematical model