Gaussian Process Nonlinear Model Predictive Control for Online Partially Observable Systems: An Application to Froth Flotation

Abstract

This paper presents a nonlinear model predictive control (NMPC) framework employing Gaussian processes (GPs) for application in froth flotation processes under online partial observability. Froth flotation, a critical process in mineral processing, involves complex, nonlinear dynamics and unmeasured variables, making traditional control methods challenging to implement. In this work, we build a data-driven control strategy by training GP-based state-space models on data generated from a physics-based model. These GP models are then integrated into an NMPC architecture where only a subset of the process states is observable online. The GP-MPC controller accounts for uncertainty and disturbances by predicting both the mean and variance of system dynamics, enabling robust optimization over a finite horizon. Results demonstrate a 20% reduction in the concentration of valuable minerals in the tailings compared to traditional control methods, while achieving consistent operation throughout the process. The framework effectively handles noise and disturbances, with the partially observable GP-MPC achieving consistent set point tracking within a 5% error margin, and reduces deviations from target values by approximately 15%. The framework also meets real-time constraints, making it well suited for complex, data-driven process control applications.