We consider an output regulation problem for a single input single output system with dynamics described by the heat equation on some bounded domain Ω⊂Rᵈ 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.
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Reis et al. (2015) studied this question.
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