Model Adaptation with Quadratic Approximation in Iterative Real-Time Optimization

Abstract

This paper deals with the iterative real-time optimization (RTO) of chemical processes under plant-model mismatch. Modifier-adaptation can cope with the plant-model mismatch by adding bias- and gradient-correction terms to the underlying model based optimization problem. These correction terms ensure the convergence to the true plant optimum via enforcing the first-order necessary-conditions of optimality of the plant despite plant-model mismatch. However, the estimation of the empirical gradients from noisy measurement data is a limiting factor and also the added correction terms do not guarantee that the second-order conditions of the optimality are satisfied upon convergence. Modifier adaptation can be combined with the quadratic approximation approach used in derivative-free optimization to ensure the convergence to the process optimum. In the framework of modifier-adaptation with quadratic approximation, this contribution proposes to add a model adaptation step such that the second-order optimality conditions are met at the plant optimum. Also to improve the estimates of the model parameters may speed up convergence. The performance of the proposed scheme is demonstrated by using a fed-batch reactor case-study.