Modifier-Adaptation Methodology for Real-Time Optimization Reformulated as a Nested Optimization Problem

Abstract

The following work presents a reformulation of the modifier-adaptation methodology for real-time optimization as a nested optimization problem. Using the idea of iteration over the modifiers, this method makes it possible to find a point that satisfies the necessary conditions of optimality (NCO) of the process, despite modeling mismatch, using an outer optimization layer that updates the gradient modifiers with the objective of minimizing the Lagrangian function estimation of the process. Moreover, if a direct search algorithm is implemented in this layer, we can find the optimum without explicitly computing the gradients of the process. The presented scheme was tested in three optimization examples, assuming the absence and presence of process noise, with parametric and structural uncertainty. The results show that in all the cases studied, the method converges to a close neighborhood of a point that satisfies the NCO of the real plant, being robust under noisy scenarios and without the need to estimate...