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Nonlinear model predictive control has become a popular approach to deal withhighly nonlinear and unsteady state systems, the performance of which canhowever deteriorate due to unaccounted uncertainties. Model predictive controlis commonly used with states from a state estimator in place of the exactstates without consideration of the error. In this paper an approach isproposed by incorporating the unscented Kalman filter into the NMPC problem,which propagates uncertainty introduced from both the state estimate andadditive noise from disturbances forward in time. The feasibility is maintainedthrough probabilistic constraints based on the Gaussian approximations of thestate distributions. The concept of robust horizon is introduced to limit theopen loop covariances, which otherwise grow too large and lead toconservativeness and infeasibility of the MPC problem. The effectiveness of theapproach was tested on a challenging semi batch reactor case study with aneconomic objective.

Stochastic Nonlinear Model Predictive Control with State Estimation by Incorporation of the Unscented Kalman Filter