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

Behzad Azmi; Karl Kunisch

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arXiv · 1901.02236

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

Behzad Azmi·Karl Kunisch

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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.

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BibTeX RIS

Behzad Azmi, Karl Kunisch. 2019-01-08. A Hybrid Finite-Dimensional RHC for Stabilization of Time-Varying Parabolic Equations. https://arxiv.org/abs/1901.02236

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