Economic Stochastic Model Predictive Control Using the Unscented Kalman Filter

Abstract

Economic model predictive control is a popular method to maximize the efficiency of a dynamic system. Often, however, uncertainties are present, which can lead to lower performance and constraint violations. In this paper, an approach is proposed that incorporates the square root Unscented Kalman filter directly into the optimal control problem to estimate the states and to propagate the mean and covariance of the states to consider noise from disturbances, parametric uncertainties and state estimation errors. The covariance is propagated up to a predefined “robust horizon” to limit open-loop covariances, and chance constraints are introduced to maintain feasibility. Often variables in chemical engineering are non-negative, which however can be violated by the Unscented Kalman filter leading to erroneous predictions. This problem is solved by log-transforming these variables to ensure consistency. The approach was verified and compared to a nominal nonlinear model predictive control algorithm on a semi-batch reactor case study with an economic objective via Monte Carlo simulations.