benmola / forecast-of-chemostat-dynamics-using-data-driven-approach

Using the Koopman Operator theory for the data-driven modeling of the Chemostat model

Forecast-of-chemostat-dynamics-using-data-driven-approach

Using the Koopman Operator theory for the data-driven modeling of the Chemostat model.

In this repo I will share with you my work on the data-driven modeling of the Chemostat system using the Koopman operator theory. This work has been published in the proccedings of the International Conference on Control, Automation and Diagnosis (ICCAD) 2021 in Gronoble France, you will find all the information in the following link : https://ieeexplore.ieee.org/document/9638749.

Abstract

This paper deals with the forecast of chemostat dynamics using a data-driven approach. We construct a datadriven model (predictor) based on the Koopman operator theory, which can predict the future state of the nonlinear dynamical system of the chemostat by only measuring the input and output of the system. We are presenting a predictor with a linear structure, that can be used for diagnostics, state estimation and future state prediction and control of nonlinear chemostat. Importantly, the method of generating such linear predictors is entirely data-driven and extremely simple, leading to nonlinear data transformation (embedding), and a linear least squares problem in the embedded space which can be readily solved for large data sets. We show in simulations that Koopman approach best predicts the system trajectories compared to a local linearization methods.

Code

The code is an adaption/extension of the code associated with the paper "Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control", Automatica 2018, by Milan Korda and Igor Mezic (available under: https://github.com/MilanKorda/KoopmanMPC).

The file named 'KoopmanChemostatModel.m' contains the main script for the work just run it and the results will show off. Others are just functions used for the main code.