Estimation of the van de Vusse reactor via Carleman embedding

TL;DR

This paper introduces a novel estimation method for the van de Vusse reactor using Carleman embedding combined with Fokker-Planck equations, leveraging Ito stochastic calculus to improve estimation accuracy in stochastic nonlinear systems.

Contribution

It unifies Carleman embedding with the Fokker-Planck equation for reactor estimation and demonstrates superior performance over the Extended Kalman Filter.

Findings

Carleman linearized estimate outperforms EKF in accuracy

Utilizes Ito stochastic calculus for stochastic system modeling

Provides a refined estimation approach for nonlinear stochastic reactors

Abstract

The van de Vusse reactor is an appealing benchmark problem in industrial control, since it has a non-minimum phase response. The van de Vusse stochasticity is attributed to the fluctuating input flow rate. The novelties of the paper are two. First, we utilize the surprising power of Ito stochastic calculus for applications to account for the van de Vusse stochasticity. Secondly, the Carleman embedding is unified with the Fokker-Planck equation for finding the estimation of the van de Vusse reactor. The revelation of the paper is that the Carleman linearized estimate of the van de Vusse reactor is more refined in contrast to the EKF predicted estimate. This paper will be useful to practitioners aspiring for formal methods for stochastically perturbed nonlinear reactors as well as system theorists aspiring for applications of their theoretical results to practical problems.