This paper investigates a new class of modifier-adaptation schemes to
overcome plant-model mismatch in real-time optimization of uncertain processes.
The main contribution lies in the integration of concepts from the areas of
Bayesian optimization and derivative-free optimization. The proposed schemes
embed a physical model and rely on trust-region ideas to minimize risk during
the exploration, while employing Gaussian process regression to capture the
plant-model mismatch in a non-parametric way and drive the exploration by means
of acquisition functions. The benefits of using an acquisition function,
knowing the process noise level, or specifying a nominal process model are
illustrated on numerical case studies, including a semi-batch photobioreactor
optimization problem.