Feasibility in Real-Time Optimization Under Model Uncertainty: The Use of Lipschitz Bounds

Abstract

In real-time optimization (RTO), feedback information from the plant is used to compensate for model uncertainty. Feasibility upon convergence can be guaranteed by simply adding bias correction terms to the constraints predicted by the model. However, the RTO solutions obtained prior to convergence may violate the plant constraints in the presence of model uncertainty. The use of constraint upper-bounding functions based on Lipschitz continuity assumptions has been proposed as a means to ensure the satisfaction of constraints. This paper presents a comparative study between three different types of Lipschitz bounds for providing theoretical feasibility guarantees in different RTO schemes. Based on a novel Lipschitz bound on the constraint modeling error, robust RTO algorithms are proposed for the two model adaptation strategies that are most commonly employed in industrial RTO practice, which are the constraint–adaptation and parameter-adaptation schemes. A robust modifier-adaptation algorithm is also studied.