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

Behzad Azmi (), Jan Rohleff () and Stefan Volkwein ()
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Behzad Azmi: University of Konstanz
Jan Rohleff: University of Konstanz
Stefan Volkwein: University of Konstanz

Chapter Chapter 3 in Model Predictive Control, 2025, pp 55-81 from Springer

Abstract: 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.

Keywords: Receding horizon control; Model-order reduction; Asymptotic stability; Optimal control; Infinite-dimensional systems; Sparse controls (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:spr:dymchp:978-3-031-85256-5_3

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DOI: 10.1007/978-3-031-85256-5_3

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