Real-Time optimization of Uncertain Process Systems via Modifier Adaptation and Gaussian Processes

In the context of static real-time optimization, the use of measurements allows dealing with uncertainty in the form of plant-model mismatch and disturbances. Modifier adaptation (MA) is a measurement-based scheme that uses first- order corrections to the model cost and constraint functions so as to achieve plant optimality upon convergence. However, first-order corrections rely crucially on the estimation of plant gradients, which typically requires costly plant experiments. The present paper proposes to implement real-time optimization via MA but use recursive Gaussian processes to represent the plant-model mismatch and estimate the plant gradients. This way, one can (i) attenuate the effect of measurement noise, and (ii) avoid plant-gradient estimation by means finite- difference schemes and, often, additional plant experiments. We use steady-state optimization data to build Gaussian-process regression functions. The efficiency of the proposed scheme is illustrated via a constrained variant of the Williams-Otto reactor problem.