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