Parameter identification for an uncertain reaction-diffusion equation via setpoint regulation

TL;DR

This paper introduces a boundary measurement-based estimator using setpoint regulation for identifying the reaction coefficient in a reaction-diffusion PDE, ensuring asymptotic convergence of both the parameter and state estimates.

Contribution

It presents a novel setpoint regulation-based estimator for reaction coefficient identification in PDEs, combining it with a state observer for comprehensive system estimation.

Findings

Estimator guarantees asymptotic convergence of reaction coefficient estimate.

Numerical example validates theoretical convergence results.

Method effectively estimates system state and parameters from boundary data.

Abstract

The problem of estimating the reaction coefficient of a system governed by a reaction-diffusion partial differential equation is tackled. An estimator relying on boundary measurements only is proposed. The estimator is based upon a setpoint regulation strategy and leads to an asymptotically converging estimate of the unknown reaction coefficient. The proposed estimator is combined with a state observer and shown to provide an asymptotic estimate of the actual system state. A numerical example supports and illustrates the theoretical results.