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Please use this identifier to cite or link to this item: http://hdl.handle.net/1807/25642

Title: Set Stabilization for Systems with Lie Group Symmetry
Authors: John, Tyson
Advisor: Maggiore, Manfredi
Department: Electrical and Computer Engineering
Keywords: set stabilization
lie group symmetry
Issue Date: 1-Jan-2011
Abstract: This thesis investigates the set stabilization problem for systems with Lie group symmetry. Initially, we examine left-invariant systems on Lie groups where the target set is a left or right coset of a closed subgroup. We broaden the scope to systems defined on smooth manifolds that are invariant under a Lie group action. Inspired by the solution of this problem for linear time-invariant systems, we show its equivalence to an equilibrium stabilization problem for a suitable quotient control system. We provide necessary and sufficient conditions for the existence of the quotient control system and analyze various properties of such a system. This theory is applied to the formation stabilization of three kinematic unicycles, the path stabilization of a particle in a gravitational field, and the conversion and temperature control of a continuously stirred tank reactor.
URI: http://hdl.handle.net/1807/25642
Appears in Collections:Master
The Edward S. Rogers Sr. Department of Electrical & Computer Engineering - Master theses

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