The ability of a model-based real-time optimization (RTO) scheme to converge to the plant optimum relies on the ability of the underlying process model to predict the plant’s necessary conditions of optimality (NCO). These include the values and gradients of the active constraints, as well as the gradient of the cost function. Hence, in the presence of plant−model mismatch or unmeasured disturbances, one could use (estimates of) the plant NCO to track the plant optimum. This paper shows how to formulate a modifed optimization problem that incorporates such information. The so-called modifiers, which express the difference between the measured or estimated plant NCO and those predicted by the model, are added to the constraints and the cost function of the modified optimization problem and are adapted iteratively. Local convergence and model-adequacy issues are analyzed. The modifier-adaptation scheme is tested experimentally via the RTO of a three-tank system.

For good performance in practice, real-time optimization schemes need to be able to deal with the inevitable plant-model mismatch problem. Unlike the two-step schemes combining parameter estimation and optimization, the modifier-adaptation approach does not require the model parameters to be estimated on-line. Instead, it uses information regarding the constraints and selected gradients to improve the plant operation. The dual modifier-adaptation approach presented in this paper drives the process towards optimality, while paying attention to the accuracy of the estimated gradients. The gradients are estimated from successive operating points generated by the optimization algorithm. The novelty lies in the development of an upper bound on the norm of the gradient errors, which is used as a constraint when determining the next operating point. The proposed approach is demonstrated via numerical simulation for both an unconstrained and a constrained problem. A Dual Modifier-Adaptation Approach forReal-Time Optimization AbstractFor good performance in practice, real-time optimization schemes need to be able to deal with the inevitable plant-model mismatch problem. Unlike the two-step schemes combining parameter estimation and optimization, the modifier-adaptation approach does not require the model parameters to be estimated on-line. Instead, it uses information regarding the constraints and selected gradients to improve the plant operation. The dual modifier-adaptation approach presented in this paper drives the process towards optimality, while paying attention to the accuracy of the estimated gradients. The gradients are estimated from successive operating points generated by the optimization algorithm. The novelty lies in the development of an upper bound on the norm of the gradient errors, which is used as a constraint when determining the next operating point. The proposed approach is demonstrated via numerical simulation for both an unconstrained and a constrained problem.

This paper presents an overview of the recent developments of modifier-adaptation schemes for real-time optimization of uncertain processes. These schemes have the ability to reach plant optimality upon convergence despite the presence of structural plant-model mismatch. Modifier Adaptation has its origins in the technique of Integrated System Optimization and Parameter Estimation, but differs in the definition of the modifiers and in the fact that no parameter estimation is required. This paper reviews the fundamentals of Modifier Adaptation and provides an overview of several variants and extensions. Furthermore, the paper discusses different methods for estimating the required gradients (or modifiers) from noisy measurements. We also give an overview of the application studies available in the literature. Finally, the paper briefly discusses open issues so as to promote future research in this area.