(197a) An Infinite Horizon Formulation of NMPC with Economic Objectives

With advances of dynamic optimization algorithms, the traditional two-layer architecture of plant operation strategy, which consists of real-time optimization and linear model predictive control (MPC) is gradually merging. Currently, there is increasing interest in economically oriented nonlinear MPC with first principle dynamic models [1,2]. In the setting of traditional set point tracking, NMPC stability is guaranteed by employing infinite horizon prediction. Although it is not practical to implement, the stability properties of the infinite horizon are usually approximated by adding a terminal constraint and terminal cost function [3]. Recently, an infinite horizon economic NMPC formulation is proposed, based on transformation of the independent time variable [4]. The practical advantage of infinite horizon prediction is that the arbitrary choice of the final time of the terminally constrained optimization horizon is avoided.

In this work, we propose an infinite horizon formulation for economic NMPC. Here we do not necessarily assume a steady state but consider a more general problem by introducing an economic objective function with periodic constraints. This is especially useful for processes that have cyclically varying inputs.

In addition to providing a stability analysis, we show that this condition allows the infinite horizon economic NMPC to be equivalent to solving an economic NMPC within finite horizon, which is implementable in practice. The proposed method is illustrated using a simulated fermentation process.

Reference: [1] S. Engell. Feedback control for optimal process operation. J. of Process Control. 2007, 17:203. [2] J.B. Rawlings and R. Amrit. Optimizing process economic performance. In Assessment and Future Directions of Nonlinear Model Predictive Control. Pavia, Italy, 2008. [3] D.Q. Mayne, J.B. Rawlings, C.V. Rao and P.O.M. Scokaert. Constrained model predictive control: stability and optimality. Automatica 2000, 36: 789. [4] L. Wurth, J.B. Rawlings and W. Marquardt. Economic dynamic real-time optimization and nonlinear model predictive control. ADCHEM, Istanbul, Turkey, 2009.