Iterative Model-Learning Scheme via Gaussian Processes for Nonlinear Model Predictive Control of (Semi-)Batch Processes
2026-04-24 • Machine Learning
Machine Learning
AI summaryⓘ
The authors developed a smart control method for batch processes, which are hard to manage because they change over time and behave nonlinearly. They use a machine learning tool called Gaussian Processes (GP) to help predict and improve control without needing a detailed physical model. By learning from each batch run, their method safely improves process performance and quickly gets close to the best possible control. Tests on a simulated chemical reactor show big improvements in product quality and quantity compared to initial methods. This approach shows it is possible to efficiently control complex batch processes using data alone.
Batch processesNonlinear model predictive control (NMPC)Gaussian Processes (GP)Model learningChance constraintsUncertainty quantificationPolymerization reactorTracking controlEconomic control objectivesSample efficiency
Authors
Tai Xuan Tan, Alexander Mitsos, Eike Cramer
Abstract
Batch processes are inherently transient and typically nonlinear, motivating nonlinear model predictive control (NMPC). However, adopting NMPC is hindered by the cost and unavailability of dynamic models. Thus, we propose to use Gaussian Processes (GP) in a model-learning NMPC scheme (GP-MLMPC) for batch processes. We initialize the GP-MLMPC using data from a single initial trajectory, e.g., from a PI controller. We iteratively apply the NMPC embedded with GPs to run batches and update the GP with new observations from each iteration, thereby achieving batch-wise improvements. Using uncertainty quantification from the GPs, we formulate chance constraints to enforce safe operation to the required confidence levels. We demonstrate our approach in \textit{silico} on a semi-batch polymerization reactor for tracking and economic objectives over durations of two hours, and the reactor temperature is constrained in a range of $\pm2^\circ C$ around its setpoint. After only four batch iterations, tracking error from the GP-MLMPC scheme converged to a reduction of $83\%$, compared to the initial trajectory. Furthermore, under an economic objective, the GP-MLMPC resulted in a 17-fold increase in final product mass by iteration 8, compared to the initial trajectory. In both cases, the resulting GP-MLMPC performance is on par with the full-model NMPC, which shows that the optimal controller can be learned by the approach. By collecting samples around the optimal trajectory, the GP-MLMPC remains sample-efficient across iterations and achieves quick convergence. Thus, the proposed GP-MLMPC scheme presents a promising data-efficient approach for the control of nonlinear batch processes without mechanistic knowledge.