Funnel control for a class of nonlinear infinite-dimensional systems

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.