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

2019/01/08 by Behzad Azmi, Karl Kunisch, Azmi, Behzad +1 · 1 citation
Engineering · #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1901.02236

openalex publication_date 2019/01/08 · openalex created_date 2022/07/30 · openalex updated_date 2026/07/28

Abstract

The present work is concerned with the stabilization of a general class of\ntime-varying linear parabolic equations by means of a finite-dimensional\nreceding horizon control (RHC). The stability and suboptimality of the\nunconstrained receding horizon framework is studied. The analysis allows the\nchoice of the squared \ℓ₁-norm as control cost. This leads to a nonsmooth\ninfinite-horizon problem which provides stabilizing optimal controls with a low\nnumber of active actuators over time. Numerical experiments are given which\nvalidate the theoretical results and illustrate the qualitative differences\nbetween the \ℓ₁- and \ℓ₂-control costs.\n

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• Stabilization of Parabolic Time-Varying PDEs using Certified Reduced-Order Receding Horizon Control

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