<?xml version="1.0" encoding="UTF-8"?><?xml-stylesheet type="text/xsl" href="static/style.xsl"?><OAI-PMH xmlns="http://www.openarchives.org/OAI/2.0/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/ http://www.openarchives.org/OAI/2.0/OAI-PMH.xsd"><responseDate>2026-09-19T00:22:22Z</responseDate><request verb="GetRecord" identifier="oai:dspace.mit.edu:1721.1/99843" metadataPrefix="dim">https://dspace.mit.edu/server/oai/request</request><GetRecord><record><header><identifier>oai:dspace.mit.edu:1721.1/99843</identifier><datestamp>2022-01-13T07:54:01Z</datestamp><setSpec>com_1721.1_7582</setSpec><setSpec>com_1721.1_7581</setSpec><setSpec>col_1721.1_131023</setSpec></header><metadata><dim:dim xmlns:dim="http://www.dspace.org/xmlns/dspace/dim" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:doc="http://www.lyncode.com/xoai" xsi:schemaLocation="http://www.dspace.org/xmlns/dspace/dim http://www.dspace.org/schema/dim.xsd">
   <dim:field mdschema="dc" element="contributor" qualifier="advisor" lang="en_US">Pablo Parrilo.</dim:field>
   <dim:field mdschema="dc" element="contributor" qualifier="author" lang="en_US">Romvary, Jordan (Jordan Joseph)</dim:field>
   <dim:field mdschema="dc" element="contributor" qualifier="other" lang="en_US">Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.</dim:field>
   <dim:field mdschema="dc" element="contributor" qualifier="department">Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science</dim:field>
   <dim:field mdschema="dc" element="date" qualifier="accessioned">2015-11-09T19:52:33Z</dim:field>
   <dim:field mdschema="dc" element="date" qualifier="available">2015-11-09T19:52:33Z</dim:field>
   <dim:field mdschema="dc" element="date" qualifier="copyright" lang="en_US">2015</dim:field>
   <dim:field mdschema="dc" element="date" qualifier="issued" lang="en_US">2015</dim:field>
   <dim:field mdschema="dc" element="identifier" qualifier="uri">http://hdl.handle.net/1721.1/99843</dim:field>
   <dim:field mdschema="dc" element="identifier" qualifier="oclc" lang="en_US">927412329</dim:field>
   <dim:field mdschema="dc" element="description" lang="en_US">Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2015.</dim:field>
   <dim:field mdschema="dc" element="description" lang="en_US">Cataloged from PDF version of thesis.</dim:field>
   <dim:field mdschema="dc" element="description" lang="en_US">Includes bibliographical references (pages 113-114).</dim:field>
   <dim:field mdschema="dc" element="description" qualifier="abstract" lang="en_US">In this thesis, we consider Witsenhausen's Counterexample, a two-stage control system in decentralized stochastic control. In particular, we investigate a specific homogenous integral equation that arises from the necessary first-order condition for optimality of the Stage I controller in the system. Using finite element (FE) analysis, we develop a numerical framework to study this integral equation and understand the structure of optimal controllers. We then solve the integral equation as a mathematical optimization and use our FE model to numerically compute a nonlinear controller that satisfies the necessary condition approximately at a set of quadrature points..</dim:field>
   <dim:field mdschema="dc" element="description" qualifier="statementofresponsibility" lang="en_US">by Jordan Romvary.</dim:field>
   <dim:field mdschema="dc" element="description" qualifier="degree" lang="en_US">S.M.</dim:field>
   <dim:field mdschema="dc" element="format" qualifier="extent" lang="en_US">114 pages</dim:field>
   <dim:field mdschema="dc" element="language" qualifier="iso" lang="en_US">eng</dim:field>
   <dim:field mdschema="dc" element="publisher" lang="en_US">Massachusetts Institute of Technology</dim:field>
   <dim:field mdschema="dc" element="rights" lang="en_US">M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.</dim:field>
   <dim:field mdschema="dc" element="rights" qualifier="uri" lang="en_US">http://dspace.mit.edu/handle/1721.1/7582</dim:field>
   <dim:field mdschema="dc" element="subject" lang="en_US">Electrical Engineering and Computer Science.</dim:field>
   <dim:field mdschema="dc" element="title" lang="en_US">A numerical study of Witsenhausen's Counterexample</dim:field>
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   	&lt;Title>A numerical study of Witsenhausen&amp;apos;s Counterexample&lt;/Title>
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   	&lt;PublicationDate>2015&lt;/PublicationDate>
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        	&lt;DisplayName&gt;Romvary, Jordan (Jordan Joseph)&lt;/DisplayName>
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    &lt;Keyword>Electrical Engineering and Computer Science.&lt;/Keyword>
   	&lt;Abstract>In this thesis, we consider Witsenhausen&amp;apos;s Counterexample, a two-stage control system in decentralized stochastic control. In particular, we investigate a specific homogenous integral equation that arises from the necessary first-order condition for optimality of the Stage I controller in the system. Using finite element (FE) analysis, we develop a numerical framework to study this integral equation and understand the structure of optimal controllers. We then solve the integral equation as a mathematical optimization and use our FE model to numerically compute a nonlinear controller that satisfies the necessary condition approximately at a set of quadrature points..&lt;/Abstract>
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