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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)

Abstract

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.

Notes

Acknowledgements

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.

References

  1. 1.
    Göttlich, S., Teuber, C.: Space mapping techniques for the optimal inflow control of transmission lines. Optim. Methods Softw. 33, 120–139 (2018)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Göttlich, S., Herty, M., Schillen, P.: Electric transmission lines: control and numerical discretization. Optim. Control Appl. Methods 37, 980–995 (2016)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Göttlich, S., Korn, R., Lux, K.: Optimal control of electricity input given an uncertain demand. Preprint (2018). arXiv:1810.05480Google Scholar
  4. 4.
    Klenke, A.: Probability Theory: A Comprehensive Course. Springer, London (2008)CrossRefGoogle Scholar
  5. 5.
    LeVeque, R.J.: Numerical methods for conservation laws. Lectures in Mathematics ETH Zürich. Birkhäuser, Basel (1990)CrossRefGoogle Scholar

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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