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Periodic Optimal Control of a Plug Flow Reactor Model with an Isoperimetric Constraint

Author

Listed:
  • Yevgeniia Yevgenieva

    (Max Planck Institute for Dynamics of Complex Technical Systems
    National Academy of Sciences of Ukraine)

  • Alexander Zuyev

    (Max Planck Institute for Dynamics of Complex Technical Systems
    National Academy of Sciences of Ukraine
    Otto von Guericke University Magdeburg)

  • Peter Benner

    (Max Planck Institute for Dynamics of Complex Technical Systems
    Otto von Guericke University Magdeburg)

  • Andreas Seidel-Morgenstern

    (Max Planck Institute for Dynamics of Complex Technical Systems
    Otto von Guericke University Magdeburg)

Abstract

We study a class of nonlinear hyperbolic partial differential equations with boundary control. This class describes chemical reactions of the type “ $$A \rightarrow $$ A → product” carried out in a plug flow reactor (PFR) in the presence of an inert component. An isoperimetric optimal control problem with periodic boundary conditions and input constraints is formulated for the considered mathematical model in order to maximize the mean amount of product over the period. For the single-input system, the optimality of a bang-bang control strategy is proved in the class of bounded measurable inputs. The case of controlled flow rate input is also analyzed by exploiting the method of characteristics. A case study is performed to illustrate the performance of the reaction model under different control strategies.

Suggested Citation

  • Yevgeniia Yevgenieva & Alexander Zuyev & Peter Benner & Andreas Seidel-Morgenstern, 2024. "Periodic Optimal Control of a Plug Flow Reactor Model with an Isoperimetric Constraint," Journal of Optimization Theory and Applications, Springer, vol. 202(2), pages 582-604, August.
    • Handle: RePEc:spr:joptap:v:202:y:2024:i:2:d:10.1007_s10957-024-02439-w
    DOI: 10.1007/s10957-024-02439-w
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