Funnel control for boundary control systems

Marc Puche; Timo Reis; Felix L. Schwenninger

doi:10.3934/eect.2020079

Article Contents

2021, Volume 10, Issue 3: 519-544. Doi: 10.3934/eect.2020079

This issue Previous Article Conditional regularity for the 3D Navier-Stokes equations in terms of the middle eigenvalue of the strain tensor Next Article Null controllability for singular cascade systems of

$ n $

-coupled degenerate parabolic equations by one control force

Funnel control for boundary control systems

1.
University of Hamburg Bundesstraße 55 20146 Hamburg Germany
2.
University of Twente P.O. Box 217 7500AE Enschede The Netherlands

^* Corresponding author: Marc Puche
^* Corresponding author: Marc Puche

Received: March 2019

Revised: June 2020

Early access: July 13, 2020

Published online: July 13, 2020

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Abstract

We study a nonlinear, non-autonomous feedback controller applied to boundary control systems. Our aim is to track a given reference signal with prescribed performance. Existence and uniqueness of solutions to the resulting closed-loop system is proved by using nonlinear operator theory. We apply our results to both hyperbolic and parabolic equations.

Keywords:

Mathematics Subject Classification: Primary: 93C20, 93C40; Secondary: 47H06.

Citation:

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Figure 1. Error evolution in a funnel $ \mathcal{F}_{\varphi} $ with boundary $ \varphi(t)^{-1} $

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Figure 2. Left: Norm of the error within the funnel boundary followed by the two reference signals and the respective outputs. Right: Inputs obtained from the feedback law

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Figure 3. Performance funnel with the error, reference signal with the output of the closed-loop system and input of the closed-loop

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Figure 4. From left to right, top to bottom, the temperature of the plate for different increasing times

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