A Distributed Parameter Approach to Optimal Filtering and Estimation with Mobile Sensor Networks

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dc.contributor.authorRautenberg, Carlos Nicolasen
dc.contributor.committeechairBurns, John A.en
dc.contributor.committeememberZietsman, Lizetteen
dc.contributor.committeememberHerdman, Terry L.en
dc.contributor.committeememberCliff, Eugene M.en
dc.contributor.committeememberBorggaard, Jeffrey T.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T20:10:22Zen
dc.date.adate2010-05-05en
dc.date.available2014-03-14T20:10:22Zen
dc.date.issued2010-03-31en
dc.date.rdate2010-05-05en
dc.date.sdate2010-04-21en
dc.description.abstractIn this thesis we develop a rigorous mathematical framework for analyzing and approximating optimal sensor placement problems for distributed parameter systems and apply these results to PDE problems defined by the convection-diffusion equations. The mathematical problem is formulated as a distributed parameter optimal control problem with integral Riccati equations as constraints. In order to prove existence of the optimal sensor network and to construct a framework in which to develop rigorous numerical integration of the Riccati equations, we develop a theory based on Bochner integrable solutions of the Riccati equations. In particular, we focus on ℐ<sub>p</sub>-valued continuous solutions of the Bochner integral Riccati equation. We give new results concerning the smoothing effect achieved by multiplying a general strongly continuous mapping by operators in ℐ<sub>p</sub>. These smoothing results are essential to the proofs of the existence of Bochner integrable solutions of the Riccati integral equations. We also establish that multiplication of continuous ℐ<sub>p</sub>-valued functions improves convergence properties of strongly continuous approximating mappings and specifically approximating C₀-semigroups. We develop a Galerkin type numerical scheme for approximating the solutions of the integral Riccati equation and prove convergence of the approximating solutions in the ℐ<sub>p</sub>-norm. Numerical examples are given to illustrate the theory.en
dc.description.degreePh. D.en
dc.identifier.otheretd-04212010-100919en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-04212010-100919/en
dc.identifier.urihttp://hdl.handle.net/10919/27103en
dc.publisherVirginia Techen
dc.relation.haspartRautenberg_CN_D_2010.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectRiccati Equationen
dc.subjectKalman Filteren
dc.subjectMobile Sensor Networksen
dc.subjectOptimal Filteringen
dc.titleA Distributed Parameter Approach to Optimal Filtering and Estimation with Mobile Sensor Networksen
dc.typeDissertationen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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