Data-Driven Self-Optimizing Control: Unconstrained Optimization Problem

Abstract

Controlled variable (CV) selection plays an important role in determining the performance of a process plant. Existing methods for CV selection through self-optimizing control requires linearization of rigorous models around nominal operating points. This is a very difficult task which results to large losses. This work presents a novel method for CV design. A necessary condition of optimality (NCO) was proposed to be the CV. The approach does not require the analytical expression of the NCO to be derived but is approximated through a single regression step based on data. Finite difference was used to approximate the NCO (gradient) using data; three finite difference schemes were employed for this purpose, which are forward, backward and central differences. Seven different cases with respect to number of sampling points, neighborhood points and finite difference schemes were investigated. To demonstrate the efficacy of the method in simplest way, it is applied to a hypothetical unconstrained optimization problem. The proposed method was found to have outperformed some existing approaches in many instances. A zero loss was recorded by some designed CVs. Central difference was found to be the best schemes among the three. Keywords— controlled variable, disturbance, finite difference, monotonicity, regression.