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

Nonlinear model predictive control (NMPC) is an effective approach for the control of nonlinear multivariable dynamic systems with constraints. However, NMPC 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 new hybrid modeling scheme is proposed to overcome this issue, which combines physical models with Gaussian process (GP) modeling. The GPs are employed to model the parts of the physical model that are difficult to describe using first principles. GPs not only give 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 and thus ensure joint probabilistic constraint satisfaction online. Advantages of our method include fast online evaluation times, 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.