English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

This paper considers the backstepping state feedback control of coupledlinear parabolic PDEs with spatially varying coefficients and bilateralactuation. By making use of the folding technique, a system representation withunilateral actuation is obtained, allowing to apply the standard backsteppingtransformation. To ensure the regularity of the solution, the folded system issubject to unusual folding boundary conditions, which lead to additionalboundary couplings between the PDEs. Therefore, the solution of thecorresponding kernel equations determining the transformations is a verychallenging problem. A systematic approach to derive the corresponding integralequations is proposed, allowing to solve them with the method of successiveapproximations. By making use of a Volterra and a Volterra-Fredholmtransformation, the closed-loop system is mapped into a cascade of stableparabolic systems. This allows a simple proof of exponential stability in the$L_2$-norm with the decay rate as design parameter. The bilateral statefeedback stabilization of an unstable system of two coupled parabolic PDEs andthe comparison to the application of an unilateral controller demonstrates theresults of the paper.

Bilateral backstepping control of coupled linear parabolic PDEs with spatially varying coefficients