Finite-dimensional controllers for robust regulation of boundary control systems

Phan Duy; Paunonen Lassi

doi:10.3934/mcrf.2020029

Article Contents

2021, Volume 11, Issue 1: 95-117. Doi: 10.3934/mcrf.2020029

This issue Previous Article Nonzero-sum differential game of backward doubly stochastic systems with delay and applications Next Article Optimal design problems governed by the nonlocal

$ p $

-Laplacian equation

Finite-dimensional controllers for robust regulation of boundary control systems

Phan Duy^1, , and
Paunonen Lassi^2,

1.
Institut für Mathematik, Leopold-Franzens-Universität Innsbruck, Technikerstraße 13/7, A-6020 Innsbruck, Austria
2.
Mathematics, Faculty of Information Technology and Communication Sciences, Tampere University, PO. Box 692, 33101 Tampere, Finland

^* Corresponding author: duy.phan-duc@uibk.ac.at
^* Corresponding author: duy.phan-duc@uibk.ac.at

Received: October 31, 2019

Revised: February 29, 2020

Early access: May 2020

Published: February 2021

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Abstract

We study the robust output regulation of linear boundary control systems by constructing extended systems. The extended systems are established based on solving static differential equations under two new conditions. We first consider the abstract setting and present finite-dimensional reduced order controllers. The controller design is then used for particular PDE models: high-dimensional parabolic equations and beam equations with Kelvin-Voigt damping. Numerical examples will be presented using Finite Element Method.

Keywords:

Mathematics Subject Classification: Primary: 93C05, 93B52, 93D09; Secondary: 35K10.

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Figure 1. Boundary controls located on red segments and regions of observations (blue)

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Figure 2. Two extensions of boundary actuators

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Figure 3. Output tracking of the boundary control of the 2D parabolic equation

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Figure 4. Hankel singular values

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Figure 5. Solutions of ODEs

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Figure 6. Output tracking of the boundary controlled beam equation with two different extensions

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