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dc.contributor.authorAguilar, Cesaren
dc.date2010-01-11 20:11:45.466
dc.date.accessioned2010-01-12T16:12:00Z
dc.date.available2010-01-12T16:12:00Z
dc.date.issued2010-01-12T16:12:00Z
dc.identifier.urihttp://hdl.handle.net/1974/5386
dc.descriptionThesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2010-01-11 20:11:45.466en
dc.description.abstractIn this thesis, we develop a feedback-invariant theory of local controllability for affine distributions. We begin by developing an unexplored notion in control theory that we call proper small-time local controllability (PSTLC). The notion of PSTLC is developed for an abstraction of the well-known notion of a control-affine system, which we call an affine system. Associated to every affine system is an affine distribution, an adaptation of the notion of a distribution. Roughly speaking, an affine distribution is PSTLC if the local behaviour of every affine system that locally approximates the affine distribution is locally controllable in the standard sense. We prove that, under a regularity condition, the PSTLC property can be characterized by studying control-affine systems. The main object that we use to study PSTLC is a cone of high-order tangent vectors, or variations, and these are defined using the vector fields of the affine system. To better understand these variations, we study how they depend on the jets of the vector fields by studying the Taylor expansion of a composition of flows. Some connections are made between labeled rooted trees and the coefficients appearing in the Taylor expansion of a composition of flows. Also, a relation between variations and the formal Campbell-Baker-Hausdorff formula is established. After deriving some algebraic properties of variations, we define a variational cone for an affine system and relate it to the local controllability problem. We then study the notion of neutralizable variations and give a method for constructing subspaces of variations. Finally, using the tools developed to study variations, we consider two important classes of systems: driftless and homogeneous systems. For both classes, we are able to characterize the PSTLC property.en
dc.format.extent737131 bytes
dc.format.mimetypeapplication/pdf
dc.language.isoengen
dc.relation.ispartofseriesCanadian thesesen
dc.rightsThis publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.en
dc.subjectnonlinear control theoryen
dc.subjectlocal controllabilityen
dc.subjectaffine distributionen
dc.subjectjet bundlesen
dc.subjectcontrol-affine systemsen
dc.subjectLie bracketen
dc.subjecthigh-order tangent vectoren
dc.titleLocal controllability of affine distributionsen
dc.typethesisen
dc.description.degreePhDen
dc.contributor.supervisorLewis, Andrew D.en
dc.contributor.departmentMathematics and Statisticsen
dc.degree.grantorQueen's University at Kingstonen


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