A robust modifier adaptation method via Hessian augmentation using model uncertainties. (March 2021) - Speakman, Jack; Papasavvas, Aris; François, Grégory
Abstract: Typical model-based optimization approaches cannot handle plant-model mismatch, therefore the use of real-time optimization (RTO) schemes which take advantage of measurements from the plant is required. Modifier adaptation (MA) uses the measurements to add a bias to the model which iteratively matches the model with the local gradient estimates of the plant, leading to satisfaction of the Karush–Kuhn–Tucker (KKT) conditions of the plant upon convergence. Whilst feasibility of the convergence solution is guaranteed, there is no such promise of the feasibility of the iterates before convergence. Some methods have been proposed which can guarantee feasibility of the iterates, however all proposed methods suffer from being extremely conservative with long convergence times and are not readily applicable without global information of the plant. This article proposes an alternative approach which uses model uncertainties to avoid the use of unobtainable information whilst removing the overly conservative iterates of previous methods. This new approach is illustrated on the Williams-Otto CSTR, illustrating rapid convergence. Highlights: Real-time optimization schemes do not generally guarantee feasible-side convergence. Modifier-adaptation scheme with improved feasibility and guaranteed model adequacy. Utilizes the uncertainty in the parameters of the plant model. Formulates an aggregate model which upper bounds the local second directional derivative of the plant model. Avoids over convexification and only uses available information of the plant.