Optimal Inflow Control Penalizing Undersupply in Transport Systems with Uncertain Demands

  • Simone Göttlich
  • Ralf Korn
  • Kerstin LuxEmail author
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 30)


We are concerned with optimal control strategies subject to uncertain demands. An Ornstein-Uhlenbeck process describes the uncertain demand. The transport within the supply system is modeled by the linear advection equation. We consider different approaches to control the produced amount at a given time to meet the stochastic demand in an optimal way. In particular, we introduce an undersupply penalty and analyze its effect on the optimal output in a numerical simulation study.



The authors are grateful for the support of the German Research Foundation (DFG) within the project “Novel models and control for networked problems: from discrete event to continuous dynamics” (GO1920/4-1) and the BMBF within the project ENets.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.University of MannheimDepartment of MathematicsMannheimGermany
  2. 2.TU KaiserslauternDepartment of MathematicsKaiserslauternGermany

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