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  <doc>
    <id>282</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2019-09-27</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Optimal Neumann boundary control of a vibrating string with uncertain initial data and probabilistic terminal constraints</title>
    <abstract language="eng">In optimal control problems, often initial data are required&#13;
that are not known exactly in practice.&#13;
In order to take into account this uncertainty,&#13;
we  consider optimal control problems for a system with an uncertain initial&#13;
state. A finite terminal time is given. On account of the uncertainty of the&#13;
initial state, it is not possible to prescribe an exact terminal state.&#13;
Instead, we are looking for controls that steer the system into a given&#13;
neighborhood of the desired terminal state with sufficiently high&#13;
probability. This neighborhood is described in terms of an inequality for&#13;
the terminal energy. The probabilistic constraint in the considered optimal&#13;
control problem leads to optimal controls that are robust against the&#13;
inevitable uncertainties of the initial state. &#13;
We show the existence of such optimal controls.&#13;
Numerical examples with&#13;
optimal Neumann control of the wave equation are presented.</abstract>
    <identifier type="doi">10.1137/19M1269944</identifier>
    <enrichment key="SubmissionStatus">in press</enrichment>
    <enrichment key="review.accepted_by">2</enrichment>
    <licence>Creative Commons - CC BY - Namensnennung 4.0 International</licence>
    <author>Mohammad Hassan Farshbaf Shaker</author>
    <author>Martin Gugat</author>
    <author>Holger Heitsch</author>
    <author>René Henrion</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>PDE constrained optimization, probabilistic constraints, uncertain initial data</value>
    </subject>
    <collection role="institutes" number="">Friedrich-Alexander-Universität Erlangen-Nürnberg</collection>
    <collection role="institutes" number="">Weierstraß-Institut für Angewandte Analysis und Stochastik</collection>
    <collection role="subprojects" number="">B04</collection>
    <collection role="subprojects" number="">C03</collection>
    <file>https://opus4.kobv.de/opus4-trr154/files/282/FGHH_2019.pdf</file>
  </doc>
</export-example>
