Forecast of chemostat dynamics using data-driven approach

This paper deals with the forecast of chemostat dynamics using a data-driven approach. We construct a data-driven 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.