Adaptive boundary control for unstable parabolic PDEs-Part II: Estimation-based designs

Authors:
Andrey Smyshlyaev;Miroslav Krstic
Affiliations:
Department of Mechanical and Aerospace Engineering, University of California at San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0411, USA;Department of Mechanical and Aerospace Engineering, University of California at San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0411, USA
Venue:
Automatica (Journal of IFAC)
Year:
2007

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Brief paper: Adaptive boundary control for unstable parabolic PDEs-Part III: Output feedback examples with swapping identifiers

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Automatica (Journal of IFAC)
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Abstract

The certainty equivalence approach to adaptive control is commonly used with two types of identifiers: passivity-based identifiers and swapping identifiers. The ''passive'' (also known as ''observer-based'') approach is the prevalent identification technique in existing results on adaptive control for PDEs but has so far not been used in boundary control problems. The swapping approach, prevalent in finite-dimensional adaptive control is employed here for the first time in adaptive control of PDEs. For a class of unstable parabolic PDEs we prove a separation principle result for both the passive and swapping identifiers combined with the backstepping boundary controllers. The result is applicable in any dimension. For physical reasons we restrict our attention to dimensions no higher than three. The results of the paper are illustrated by simulations.