Optimal Control of Nonlinear Hyperbolic Conservation Laws with Switching

  • Sebastian PfaffEmail author
  • Stefan Ulbrich
  • Günter Leugering
Part of the International Series of Numerical Mathematics book series (ISNM, volume 165)


We consider optimal control problems governed by nonlinear hyperbolic conservation laws at junctions and analyze in particular the Fréchet-differentiability of the reduced objective functional. This is done by showing that the control-to-state mapping of the considered problems satisfies a generalized notion of differentiability. We consider both, the case where the controls are the initial and the boundary data as well as the case where the system is controlled by the switching times of the node condition. We present differentiability results for the considered problems in a quite general setting including an adjoint-based gradient representation of the reduced objective function.


Optimal control Scalar conservation law Network 



The authors gratefully acknowledge the support of the German Research Foundation (DFG) within the Priority Program 1253 “Optimization with Partial Differential Equations” under grant UL158/8-1. Moreover, we gratefully acknowledge discussions with T. I. Seidman.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Sebastian Pfaff
    • 1
    Email author
  • Stefan Ulbrich
    • 1
  • Günter Leugering
    • 2
  1. 1.Department of MathematicsTechnische Universität DarmstadtDarmstadtGermany
  2. 2.Department of MathematicsUniversität Erlangen-NürnbergErlangenGermany

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