Funnel Control for the Boundary Controlled Heat Equation

We consider an output regulation problem for a single input single output system with dynamics described by the heat equation on some bounded domain $\Omega\subset{\mathbb{R}} delta $ with sufficiently smooth boundary. The input is formed by Neumann boundary control, and the output is the surface in...

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Bibliographic Details
Published in:SIAM journal on control and optimization 2015-01, Vol.53 (1), p.547-574
Main Authors: Reis, Timo, Selig, Tilman
Format: Article
Language:English
Subjects:
Boundaries
Boundary control
Control
Dynamical systems
Dynamics
Funnels
Heat equations
Optimization
Reference signals
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Summary:We consider an output regulation problem for a single input single output system with dynamics described by the heat equation on some bounded domain $\Omega\subset{\mathbb{R}} delta $ with sufficiently smooth boundary. The input is formed by Neumann boundary control, and the output is the surface integral of the state at the boundary. We show that the funnel controller can be applied to this system in order to track a given output reference signal within a prespecified performance funnel.
ISSN:0363-0129
1095-7138
DOI:10.1137/140971567