Sufficient Conditions for Feasibility and Optimality of Real-Time Optimization Schemes - I. Theoretical Foundations

TL;DR

This paper develops theoretical conditions to ensure the feasibility and optimality of real-time optimization algorithms, providing a unified framework that guarantees safe convergence to the true process optimum.

Contribution

It introduces a set of sufficient conditions (SCFO) for real-time optimization that can be applied to any algorithm to guarantee safety and optimality.

Findings

SCFO enforce feasible convergence in numerical examples

Algorithms with SCFO outperform those without in safety-critical scenarios

Theoretical foundation for unified real-time optimization guarantees

Abstract

The idea of iterative process optimization based on collected output measurements, or "real-time optimization" (RTO), has gained much prominence in recent decades, with many RTO algorithms being proposed, researched, and developed. While the essential goal of these schemes is to drive the process to its true optimal conditions without violating any safety-critical, or "hard", constraints, no generalized, unified approach for guaranteeing this behavior exists. In this two-part paper, we propose an implementable set of conditions that can enforce these properties for any RTO algorithm. The first part of the work is dedicated to the theory behind the sufficient conditions for feasibility and optimality (SCFO), together with their basic implementation strategy. RTO algorithms enforcing the SCFO are shown to perform as desired in several numerical examples - allowing for feasible-side convergence to the plant optimum where algorithms not enforcing the conditions would fail.