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Iterative optimization using gradient modifiers

Iterative online optimization via modifier adaptation

Iterative optimization is a strategy for improving the operation of cyclic or batch processes and for optimizing the operation of slow, essentially stationary processes (also called real-time optimization, RTO). Traditionally, real-time optimization is based upon rigorous nonlinear process models and adjusts the set-points of key process variables to optimize the economic performance while meeting constraints on product properties and operational limits. As for any model-based optimization scheme, a key issue is the accuracy of the model that is used in the optimization. Due to plant-model mismatch, the optimum of the real plant may differ considerably from the optimum that is computed for the model. Furthermore, the constraints may be violated by the theoretically optimal set-point.
Iterative optimization via modifier adaptation combines the use of models and of the data collected during the operation of the plant. The gradients of the cost function and the values and the gradients of the constraints are modified based on the information that was obtained at the previous set-points or from the previous batches. This correction ensures convergence to the true plant optimum and satisfaction of the constraints by the real process.
This technique has been demonstrated to be efficient for batch chromatography and other chromatographic processes (annular chromatography, MCSGP-process) in previous work of our group.

Currently, we are applying the iterative optimization with modifier adaptation to the online optimization of the operating conditions of the miniplants for the hydroformylation of n-Dodecene that are operated in the SFB Transregio InPROMPT at TU Berlin and TU Dortmund.


Gao, W., Engell, S.: Iterative set-point optimization of batch chromatography. Comput. Chem. Eng., 29(6), 2005, 1401–1409.

Behrens, M., Khobkhun, P., Potschka, A., Engell, S.: Optimizing set point control if the MCSGP process. In: Proc. of the 13th European Control Conference (ECC), Strasbourg, 2014, 1139–1144.

Iterative optimizing control by modifier adaptation with quadratic approximation

MOBOCON_logo_smallThere is a fundamental problem with the use of the gradient modifiers in iterative optimization: the difficulty to correctly estimate the true plant gradients from the available measured data which has to be done by some sort of finite-difference approximation. We have therefore developed a new modifier adaptation scheme that uses ideas from derivative-free optimization (DFO).
The new scheme combines the quadratic approximation that is used in DFO with the modifier adaptation approach and integrates recent advances in both areas. DYN_brochure_S8Quadratic approximations of the cost function and of the constraints are constructed based on screened data, and the gradients with respect to the manipulated variables are computed from these approximated models. The next set-point move is then determined by modifier-adapted optimization in which the model is corrected by the empirical gradient information. Simulation studies have shown that the scheme leads to faster and more robust convergence to the true optimum and suppresses the oscillations around the optimum that are observed when using finite difference approximations. In future work, we will explore how to extend the scheme to updates during plant transients.


Gao, W., Wenzel, S., Engell, S.: Modifier Adaptation with Quadratic Approximation in Iterative Optimizing Control. In: Proc. of the 14th European Control Conference (ECC), Linz, 2015, 2532–2537.

Gao, W., Wenzel, S., Engell, S.: Integration of Gradient Adaptation and Quadratic Approximation in Real-Time Optimization. In: Proc. of the 34th Chinese Control Conference, Hangzhou, 2015, 2780–2785.