dc.contributor.author Aguilar, Cesar en dc.date 2010-01-11 20:11:45.466 dc.date.accessioned 2010-01-12T16:12:00Z dc.date.available 2010-01-12T16:12:00Z dc.date.issued 2010-01-12T16:12:00Z dc.identifier.uri http://hdl.handle.net/1974/5386 dc.description Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2010-01-11 20:11:45.466 en dc.description.abstract In 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. en 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. dc.format.extent 737131 bytes dc.format.mimetype application/pdf dc.language.iso eng en dc.relation.ispartofseries Canadian theses en dc.rights This 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.subject nonlinear control theory en dc.subject local controllability en dc.subject affine distribution en dc.subject jet bundles en dc.subject control-affine systems en dc.subject Lie bracket en dc.subject high-order tangent vector en dc.title Local controllability of affine distributions en dc.type thesis en dc.description.degree PhD en dc.contributor.supervisor Lewis, Andrew D. en dc.contributor.department Mathematics and Statistics en dc.degree.grantor Queen's University at Kingston en
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