Hybrid Gaussian Process Modeling Applied to Economic Stochastic Model Predictive Control of Batch Processes

Abstract

Nonlinear model predictive control (NMPC) is an efficient approach for the control of nonlinear multivariable dynamic systems with constraints, which however requires an accurate plant model. Plant models can often be determined from first principles, parts of the model are however difficult to derive using physical laws alone. In this paper a hybrid Gaussian process (GP) first principles modeling scheme is proposed to overcome this issue, which exploits GPs to model the parts of the dynamic system that are difficult to describe using first principles. GPs not only give accurate predictions, but also quantify the residual uncertainty of this model. It is vital to account for this uncertainty in the control algorithm, to prevent constraint violations and performance deterioration. Monte Carlo samples of the GPs are generated offline to tighten constraints of the NMPC to ensure joint probabilistic constraint satisfaction online. Advantages of our method include fast online evaluation times, possibility to account for online learning alleviating conservativeness, and exploiting the flexibility of GPs and the data efficiency of first principle models. The algorithm is verified on a case study involving a challenging semi-batch bioreactor.

Industrial data science – a review of machine learning applications for chemical and process industries

“…discrepancy models). 16 Fig. 1 Contrary to the traditional approach, where first principles models are used, machine learning fits empirical models using experimental data (training data).…”

“…discrepancy models. 16 For example, if a heat or mass balance can foresee issues in quality or productivity, predictors that are part of these terms will be immediately found. Simply removing them from the input list will not change the variability on the target, so a better approach is to focus on explaining the residuals.…”

“…Fig 16. Compressor characteristic (a) and spectrogram (b) are two traditional approaches to detect inefficient or anomaly operating modes.…”

Machine learning‐based model predictive controller design for cell culture processes

“…The poor quality of linear models (measured through one‐step ahead prediction accuracy) may impact the quality of control by providing suboptimal control designs (Rashedi et al, 2022). GP has played the role of forecast model in the MPC for controlling batch (Bradford et al, 2021) and continuous (Kocijan et al, 2004) processes. The powerful statistical representation of GP enables the model to grasp complex nonlinear process dynamics efficiently.…”

A model‐and data‐driven predictive control approach for tracking of stochastic nonlinear systems using Gaussian processes

“…presents an MPC approach that integrates a nominal system with an additive nonlinear part of the dynamics modeled as a GP. A data‐driven SNMPC approach which relies on black‐box identification of a GP model from input/output data pairs to account for the state dependency of the uncertainty is proposed in References 41 and 48, which generates Monte Carlo samples of the GP offline for constraint tightening using back‐offs.…”