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

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.