  Nonlinear model predictive control (NMPC) is an efficient approach for the
control of nonlinear multivariable dynamic systems with constraints, which
however 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 hybrid Gaussian process (GP) first
principles modeling scheme is proposed to overcome this issue, which exploits
GPs to model the parts of the dynamic system that are difficult to describe
using first principles. GPs not only give accurate 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 to ensure joint probabilistic constraint
satisfaction online. Advantages of our method include fast online evaluation
times, possibility to account for online learning alleviating conservativeness,
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.
