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.
| Identifer | oai:union.ndltd.org:TORONTO/oai:tspace.library.utoronto.ca:1807/25642 |
| Date | 01 January 2011 |
| Creators | John, Tyson |
| Contributors | Maggiore, Manfredi |
| Source Sets | University of Toronto |
| Language | en_ca |
| Detected Language | English |
| Type | Thesis |
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