Funnel control for a class of nonlinear infinite-dimensional systems

Anthony Hastir; Joseph J. Winkin; Denis Dochain

doi:10.1016/j.automatica.2023.110964

Funnel control for a class of nonlinear infinite-dimensional systems

Anthony Hastir, Joseph J. Winkin, Denis Dochain

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	110964
Journal	Automatica
Volume	152
DOIs	https://doi.org/10.1016/j.automatica.2023.110964
Publication status	Published - Jun 2023

Funding

This research was conducted with the financial support of F.R.S-FNRS, Belgium . Anthony Hastir is a FNRS Research Fellow under the grant FC 29535 . The scientific responsibility rests with its authors. The material in this paper was presented at the IFAC CPDE 2022 Workshop on Control of Systems Governed by Partial Differential Equations, Kiel, Germany, September 7–9, 2022. This paper was recommended for publication in revised form by Associate Editor Rafael Vazquez under the direction of Editor Miroslav Krstic. This research was conducted with the financial support ofF.R.S-FNRS, Belgium . Anthony Hastir is a FNRS Research Fellow under the grant FC 29535. The scientific responsibility rests with its authors. The material in this paper was presented at the IFAC CPDE 2022 Workshop on Control of Systems Governed by Partial Differential Equations, Kiel, Germany, September 7–9, 2022. This paper was recommended for publication in revised form by Associate Editor Rafael Vazquez under the direction of Editor Miroslav Krstic.

Funders	Funder number
Fonds de la Recherche Scientifique F.R.S.-FNRS	FC 29535
Fonds de la Recherche Scientifique F.R.S.-FNRS

Keywords

Funnel control
Nonlinear distributed parameter systems
Plug-flow tubular reactor
Sine–Gordon equation

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10.1016/j.automatica.2023.110964

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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.",

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AB - 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.

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Funnel control for a class of nonlinear infinite-dimensional systems

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