APPROXIMATING REACHABLE SETS FOR A CLASS OF LINEAR SYSTEMS SUBJECT TO BOUNDED CONTROL.

Persistent Link:
http://hdl.handle.net/10150/187645
Title:
APPROXIMATING REACHABLE SETS FOR A CLASS OF LINEAR SYSTEMS SUBJECT TO BOUNDED CONTROL.
Author:
GAYEK, JONATHAN EDWARD.
Issue Date:
1984
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
A method is proposed for approximating the reachable set from the origin for a class of n first order linear ordinary differential equations subject to bounded control. The technique involves decoupling the system equations into 1- and 2-dimensional linear subsystems, and then finding the reachable set of each of the subsystems. Having obtained bounds on each of the decoupled state variables, a n-dimensional parallelpiped is constructed which contains the reachable set from the origin for the original system. Several illustrative examples are presented for the case where the control is a scalar. The technique is also compared to a Lyapunov approach of approximating the reachable set in a simple 2-dimensional example.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Set theory.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Applied Mathematics; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Vincent, Thomas L.

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleAPPROXIMATING REACHABLE SETS FOR A CLASS OF LINEAR SYSTEMS SUBJECT TO BOUNDED CONTROL.en_US
dc.creatorGAYEK, JONATHAN EDWARD.en_US
dc.contributor.authorGAYEK, JONATHAN EDWARD.en_US
dc.date.issued1984en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractA method is proposed for approximating the reachable set from the origin for a class of n first order linear ordinary differential equations subject to bounded control. The technique involves decoupling the system equations into 1- and 2-dimensional linear subsystems, and then finding the reachable set of each of the subsystems. Having obtained bounds on each of the decoupled state variables, a n-dimensional parallelpiped is constructed which contains the reachable set from the origin for the original system. Several illustrative examples are presented for the case where the control is a scalar. The technique is also compared to a Lyapunov approach of approximating the reachable set in a simple 2-dimensional example.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectSet theory.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineApplied Mathematicsen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorVincent, Thomas L.en_US
dc.identifier.proquest8412663en_US
dc.identifier.oclc690917876en_US
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