  An adaptive funnel control method is considered for the regulation of the
output for a class of nonlinear infinite-dimensional systems on real Hilbert
spaces. After a decomposition of the state space and some change of variables
related to the Byrnes-Isidori form, it is shown that the funnel controller
presented in (Berger et al., 2020) achieves the control objective under some
assumptions on the nonlinear system dynamics, like well-posedness and
Bounded-Input-State Bounded-Output (BISBO) stability. The theory is applied to
the regulation of the temperature in a chemical plug-flow tubular reactor whose
reaction kinetics are modeled by the Arrhenius nonlinearity. Furthermore a
damped sine-Gordon model is shown to fit the required assumptions as well. The
theoretical results are illustrated by means of numerical simulations.
