Scaling Gaussian Processes for Deterministic Model Predictive Control with Online Updates: A Framework for Model...

Gaussian processes (GPs) are powerful, nonparametric models, widely recognized as universal function approximators due to their ability to provide robust probabilistic predictions alongside quantified uncertainty estimates. This has allowed for the modeling of complex processes in chemical engineering with applications to process optimization, prediction, and control. However, the practical adoption of standard GPs is severely constrained by their computational training complexity $O\left(n^3\right)$ . This bottleneck is particularly problematic in modern high-throughput environments, such as those associated with Industry 4.0, big data applications, and advanced manufacturing. Addressing this demand requires the implementation of highly efficient online learning and model updating strategies. This paper specifically looks at deterministic nonlinear Model Predictive Control (MPC) and proposes a framework for efficiently identifying a highly performant Gaussian process approximation model and re-identification metric, alongside stability and feasibility analyses. The effectiveness of these techniques in a real-time system is demonstrated through a cascaded tanks experiment.