Optimal Control of Nonlinear Hyperbolic Conservation Laws with Switching

  • Sebastian Pfaff
  • Stefan Ulbrich
  • Günter Leugering
Chapter

Abstract

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.

Keywords

Optimal control Scalar conservation law Network 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

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

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