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This chapter deals with the stabilization of a class of linear time-varyingparabolic partial differential equations employing receding horizon control(RHC). Here, RHC is finite-dimensional, i.e., it enters as a time-dependinglinear combination of finitely many indicator functions whose total supportscover only a small part of the spatial domain. Further, we consider the squaredl1-norm as the control cost. This leads to a nonsmooth infinite-horizon problemwhich allows a stabilizing optimal control with a low number of activeactuators 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. Numericalexperiments are also reported which illustrate the advantages of our MORapproaches.

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