Economic Multi-stage Output Feedback NMPC using the Unscented Kalman Filter

Nonlinear Model predictive control (NMPC) is a popular control strategy for highly nonlinear chemical processes. The ability to handle safety and environmental constraints along with the use of an economic objective makes NMPC highly appealing to industries. The performance of NMPC depends strongly on the accuracy of the model. In reality, there always are plant-model mismatch and state estimation errors. Hence the NMPC controller must be robust to uncertainties in the model as well as against estimation errors. Among the several approaches presented in the literature, the scenario-tree based multi-stage NMPC approach is a non-conservative and efficient formulation. In this approach, the evolutions of the plant for different realizations of the uncertainties are considered as different scenarios and the optimization problem is formulated as a multi-stage stochastic programming problem with recourse. In this work, we consider multi-stage output feedback NMPC using the Unscented Kalman Filter (UKF) where the nonlinearities are represented using deterministically chosen sigma points for state estimation. In the control problem, we explicitly consider the UKF estimation equations to predict the future evolution of the system. The proposed approach is illustrated by simulation results of fed-batch chemical reactor with an economic cost function.