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Nonlinear model predictive control (NMPC) is an efficient approach for thecontrol of nonlinear multivariable dynamic systems with constraints, whichhowever requires an accurate plant model. Plant models can often be determinedfrom first principles, parts of the model are however difficult to derive usingphysical laws alone. In this paper a hybrid Gaussian process (GP) firstprinciples modeling scheme is proposed to overcome this issue, which exploitsGPs to model the parts of the dynamic system that are difficult to describeusing first principles. GPs not only give accurate predictions, but alsoquantify the residual uncertainty of this model. It is vital to account forthis uncertainty in the control algorithm, to prevent constraint violations andperformance deterioration. Monte Carlo samples of the GPs are generated offlineto tighten constraints of the NMPC to ensure joint probabilistic constraintsatisfaction online. Advantages of our method include fast online evaluationtimes, possibility to account for online learning alleviating conservativeness,and exploiting the flexibility of GPs and the data efficiency of firstprinciple models. The algorithm is verified on a case study involving achallenging semi-batch bioreactor.

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