Design of continuous-time flows on intertwined orbit spaces
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Absil, P-A; Lageman, Christian; Manton, Jonathan
Description
Consider a space M endowed with two or more Lie group actions. Under a certain condition on the orbits of the Lie group actions, we show how to construct a flow on M that projects to prescribed flows on the orbit spaces of the group actions. Hence, in order to design a flow that converges to the intersection of given orbits, it suffices to design flows on the various orbit spaces that display convergence to the desired orbits, and then to lift these flows to M using the proposed procedure. We...[Show more]
dc.contributor.author | Absil, P-A | |
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dc.contributor.author | Lageman, Christian | |
dc.contributor.author | Manton, Jonathan | |
dc.coverage.spatial | New Orleans USA | |
dc.date.accessioned | 2015-12-08T22:36:20Z | |
dc.date.created | December 12-14 2007 | |
dc.identifier.isbn | 1424414989 | |
dc.identifier.uri | http://hdl.handle.net/1885/35212 | |
dc.description.abstract | Consider a space M endowed with two or more Lie group actions. Under a certain condition on the orbits of the Lie group actions, we show how to construct a flow on M that projects to prescribed flows on the orbit spaces of the group actions. Hence, in order to design a flow that converges to the intersection of given orbits, it suffices to design flows on the various orbit spaces that display convergence to the desired orbits, and then to lift these flows to M using the proposed procedure. We illustrate the technique by creating a flow for principal component analysis. The flow projects to a flow on the Grassmann manifold that achieves principal subspace analysis and to a flow on the "shape" manifold that converges to the set of orthonormal matrices. | |
dc.publisher | Institute of Electrical and Electronics Engineers (IEEE Inc) | |
dc.relation.ispartofseries | IEEE Conference on Decision and Control 2007 | |
dc.source | Proceedings of the 46th IEEE Conference on Decision and Control 2007 | |
dc.subject | Keywords: Orbits; Principal component analysis; Systems analysis; Orbit spaces; Orthonormal matrices; Principal subspace analysis; Continuous time systems | |
dc.title | Design of continuous-time flows on intertwined orbit spaces | |
dc.type | Conference paper | |
local.description.notes | Imported from ARIES | |
local.description.refereed | Yes | |
dc.date.issued | 2007 | |
local.identifier.absfor | 010203 - Calculus of Variations, Systems Theory and Control Theory | |
local.identifier.ariespublication | u3169606xPUB122 | |
local.type.status | Published Version | |
local.contributor.affiliation | Absil, P-A, Catholic University of Louvain | |
local.contributor.affiliation | Lageman, Christian, College of Physical and Mathematical Sciences, ANU | |
local.contributor.affiliation | Manton, Jonathan, College of Engineering and Computer Science, ANU | |
local.description.embargo | 2037-12-31 | |
local.bibliographicCitation.startpage | 6244 | |
local.bibliographicCitation.lastpage | 6249 | |
local.identifier.doi | 10.1109/CDC.2007.4434712 | |
dc.date.updated | 2016-02-24T09:52:38Z | |
local.identifier.scopusID | 2-s2.0-62749122909 | |
Collections | ANU Research Publications |
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