Approximation of the LQR control problem for systems governed by partial functional differential equations

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dc.contributor.authorMiller, Robert Edwinen
dc.contributor.committeechairBurns, John A.en
dc.contributor.committeememberHerdman, Terry L.en
dc.contributor.committeememberWheeler, Roberten
dc.contributor.committeememberCliff, Eugene M.en
dc.contributor.committeememberHannsgen, Kenneth B.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2015-06-24T13:35:17Zen
dc.date.available2015-06-24T13:35:17Zen
dc.date.issued1988en
dc.description.abstractWe present an abstract framework for state space formulation and a generalized theorem on well-posedness which can be applied to a class of partial functional differential equations which arise in the modeling of viscoelastic and certain thermo-viscoelastic systems. Examples to which the theory applies include both second- and fourth-order equations with a variety of boundary conditions. The theory presented here allows for singular kernels as well as flexibility in the choice of state space. We discuss an approximation scheme using spline in the spatial variable and an averaging scheme in the delay variable. We compare a uniform mesh to a nonuniform mesh and give numerical results which indicate that the non-uniform mesh, which gives a better approximation of the kernel near the singularity, yields faster convergence. We give a proof of convergence of the simulation problem for singular kernels and of the control problem for bounded kernels. We use techniques of semigroup theory to establish the results on well-posedness and convergence.en
dc.description.degreePh. D.en
dc.format.extentiv, 95 leavesen
dc.format.mimetypeapplication/pdfen
dc.identifier.urihttp://hdl.handle.net/10919/53588en
dc.language.isoen_USen
dc.publisherVirginia Polytechnic Institute and State Universityen
dc.relation.isformatofOCLC# 19736067en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.lccLD5655.V856 1988.M547en
dc.subject.lcshDifferential equations, Partialen
dc.subject.lcshEquations, Quadraticen
dc.titleApproximation of the LQR control problem for systems governed by partial functional differential equationsen
dc.typeDissertationen
dc.type.dcmitypeTexten
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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