Economic model predictive control (EMPC) is an efficient method to address process control problems integrated with dynamic economic optimization of the process [1]. EMPC continuously operates a chemical process in a time-varying fashion (off steady-state) to dynamically optimize process economic performance beyond what can be achieved via steady-state operation, and it also incorporates constraints to guarantee closed-loop stability within a well-characterized region of the operating state-space. Since the performance of EMPC in terms of closed-loop stability and economic benefits depends heavily on an accurate process model for predicting future states, in this work, we focus on the development of a well-fitting recurrent neural network (RNN) model that is able to capture system nonlinear dynamics in a given operating region. Specifically, based on the dataset generated from extensive open-loop simulations under different control inputs (including the use of classical feedback control in the case of operation around an unstable equilibrium point) within the targeted operation region, RNN models are first developed to guarantee that the modeling error between the RNN model and the actual nonlinear process model is sufficiently small [2,3]. Then, the RNN model is incorporated in the formulation of Lyapunov-based EMPC (LEMPC), under which, the stability analysis of the closed-loop system demonstrates the boundedness of closed-loop state in the stability region [4]. Additionally, to further improve the prediction accuracy of the RNN model, ensemble regression models are utilized in LEMPC and parallel computing is introduced to reduce real-time computation time [4] of the model solution. The proposed LEMPC using RNN models is applied to a chemical process example to demonstrate its closed-loop stability and economic performance as well as significant computational advantages under parallel operation. Comparisons of the RNN model in terms of accuracy and resulting closed-loop performance with other data-based modeling techniques (e.g., linear state-space identification) are made to demonstrate its usefulness in the case of significant nonlinear behavior.
[1] Ellis, M., Durand, H., Christofides, P.D. A tutorial review of economic model predictive control methods. Journal of Process Control. 2014, 24:1156-1178.
[2] Kosmatopoulos, E. B., Polycarpou, M. M., Christodoulou, M. A., and Ioannou, P. A. (1995). High-order neural network structures for identification of dynamical systems. IEEE transactions on Neural Networks, 6, 422-431.
[3] Polycarpou, M. M., and Ioannou, P. A. Identification and control of nonlinear systems using neural network models: Design and stability analysis. University of Southern Calif, 1991.
[4] Alanqar, A., Durand, H., and Christofides, P. D. On Identification of Well-Conditioned Nonlinear Systems: Application to Economic Model Predictive Control of Nonlinear Processes. AIChE J., 61, 3353-3373, 2015.
