A dual modifier-adaptation approach for real-time optimization

Abstract

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.

Control and Optimization of Batch Chemical Processes

“…First, the identification problem requires sufficient excitation, which is however rarely the case since the inputs are computed for optimality rather than for the sake of identification. Hence, one has to make sure that there is sufficient excitation, for example via a dual optimization approach that adds a constraint to the optimization problem regarding the accuracy of the estimated parameters 89 . The second limitation is inherent to the philosophy of the method.…”

Extension of modifier adaptation for controlled plants using static open-loop models

“…We will use the model from [29], which has become a standard test problem for real-time optimization techniques [16]. Although the original problem is an open-loop reactor, the aim is here to optimize the reactor in closed-loop operation.…”

“…This is a very valuable property since structural mismatch is almost invariably present in complex plants (i.e., there are always simplifying assumptions made during the modeling stage). However, experimental gradients must be estimated for the plant, an onerous task that has received much attention in the literature in recent years [16,17].…”

From Discrete Measurements to Bounded Gradient Estimates: A Look at Some Regularizing Structures

“…When the input set is not fixed and can be changed (as is the case in optimization 7,8 ), this behavior should motivate the user to choose input points that are somehow favorable to this regularization.…”

“…3 The authors' own interest in the problem comes from its applicability to real-time optimization, 4,5,6,7 where the objective is to steer a process towards economically optimal conditions while working only with discrete measurements -using, for example, a gradient-descent method. We also note that this problem may play an important role, for almost identical reasons, in numerical black-box optimization when function evaluations are time consuming.…”