Unsolved Problems in Mathematical Systems and Control Theory by Blondel Vincent D.; Megretski Alexandre; Blondel Vincent D. D

Author:Blondel, Vincent D.; Megretski, Alexandre; Blondel, Vincent D. D.
Language: eng
Format: epub
Publisher: Princeton University Press
Published: 2009-03-14T16:00:00+00:00

PART 5

Distributed Parameter Systems

Problem 5.1

Infinite dimensional backstepping for

nonlinear parabolic PDEs

Andras Balogh and Miroslav Krstic

Department of MAE

University of California at San Diego

La Jolla, CA 92093–0411

USA

[email protected] and [email protected]

1 INTRODUCTION

This note explores an approach to global stabilization of boundary controlled nonlinear PDEs by a technique inspired by finite dimensional back-stepping/ feedback linearization. Solution of the problem presented herein would be of enormous significance because these are the only truly constructive and systematic techniques in finite dimension.

We consider nonlinear parabolic PDEs of the form

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