<?xml version="1.0" encoding="utf-8"?>
<export-example>
  <doc>
    <id>85</id>
    <completedYear>2017</completedYear>
    <publishedYear>2016</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>904</pageFirst>
    <pageLast>939</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>32</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>1</belongsToBibliography>
    <completedDate>2016-10-11</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Optimal Control of Nonlinear Hyperbolic Conservation Laws by On/Off-Switching</title>
    <abstract language="eng">This paper studies the differentiability properties of the control-to-state mapping for entropy solutions to a scalar hyperbolic conservation law on R with respect to the switching times of an on/off-control. The switching times between on-modes and off-modes are the control variables of the considered optimization problem, where a general tracking-type functional is minimized.We investigate the differentiability of the reduced objective function, also in the presence of shocks. We show that the state y(t,·)  at some observation time t depends differentiably on the switching times in a generalized sense that implies total differentiability for the composition with a tracking functional. Furthermore, we present an adjoint-based formula for the gradient of the reduced objective functional with respect to the switching times.</abstract>
    <parentTitle language="eng">Optimization Methods and Software</parentTitle>
    <identifier type="doi">10.1080/10556788.2016.1236796</identifier>
    <enrichment key="SubmissionStatus">in press</enrichment>
    <author>Sebastian Pfaff</author>
    <author>Stefan Ulbrich</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal control, scalar conservation law, network</value>
    </subject>
    <collection role="institutes" number="">Technische Universität Darmstadt</collection>
    <collection role="subprojects" number="">A02</collection>
  </doc>
</export-example>
