Adaptive output error feedback for a class of nonlinear infinite-dimensional systems

TL;DR

This paper develops an adaptive funnel control approach for nonlinear infinite-dimensional systems, demonstrating its effectiveness through theoretical analysis and numerical simulations on chemical reactors and sine-Gordon models.

Contribution

It extends funnel control methods to a class of nonlinear infinite-dimensional systems with new theoretical guarantees and practical applications.

Findings

Successful regulation of temperature in a chemical reactor.

Validation of the control method on a sine-Gordon model.

Numerical simulations confirm theoretical results.

Abstract

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.