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Finite-Dimensional Receding Horizon Control of Linear Time-Varying Parabolic PDEs: Stability Analysis and Model-Order Reduction

Author

Listed:
  • Behzad Azmi

    (University of Konstanz)

  • Jan Rohleff

    (University of Konstanz)

  • Stefan Volkwein

    (University of Konstanz)

Abstract

This chapter deals with the stabilization of a class of linear time-varying parabolic partial differential equations employing receding horizon control (RHC). Here, RHC is finite-dimensional, i.e., it enters as a time-depending linear combination of finitely many indicator functions whose total supports cover only a small part of the spatial domain. Further, we consider the squared $$\ell _1$$ -norm as the control cost. This leads to a nonsmooth infinite-horizon problem which allows a stabilizing optimal control with a low number of active actuators over time. First, the stabilizability of RHC is investigated. Then, to speed up numerical computation, the data-driven model-order reduction (MOR) approaches are adequately incorporated within the RHC framework. Numerical experiments are also reported which illustrate the advantages of our MOR approaches.

Suggested Citation

  • Behzad Azmi & Jan Rohleff & Stefan Volkwein, 2025. "Finite-Dimensional Receding Horizon Control of Linear Time-Varying Parabolic PDEs: Stability Analysis and Model-Order Reduction," Dynamic Modeling and Econometrics in Economics and Finance,, Springer.
    • Handle: RePEc:spr:dymchp:978-3-031-85256-5_3
    DOI: 10.1007/978-3-031-85256-5_3
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