A Hybrid Finite-Dimensional RHC for Stabilization of Time-Varying Parabolic Equations

Abstract

The present work is concerned with the stabilization of a general class of time-varying linear parabolic equations by means of a finite-dimensional receding horizon control (RHC). The stability and suboptimality of the unconstrained receding horizon framework is studied. The analysis allows the choice of the squared ${\ell }_1$-norm as control cost. This leads to a nonsmooth infinite-horizon problem which provides stabilizing optimal controls with a low number of active actuators over time. Numerical experiments are given which validate the theoretical results and illustrate the qualitative differences between the ${\ell }_1$- and ${\ell }_2$-control costs.