Efficient dynamic optimization for nonlinear model predictive control-application to a high-density poly-ethylene grade change problem

Nonlinear model predictive control (NMPC) is believed to play an important role in improving the quality and flexibility of the production of many chemical plants. More widespread application can be expected when systematic solutions are found for modeling large-scale nonlinear processes and for efficient solution of the dynamic optimization problems NMPC entails. The control parametrization approach to dynamic optimization solves the dynamic optimization problem as a nonlinear program using e.g. the sequential quadratic program (SQP) in the outer loop optimization problem. In the SQP approach, a reduced space quadratic program is set up based on a quasi-Newton method estimate of the Hessian. We propose, based on an investigation of the structure of the Hessian of the NMPC problem, a different Hessian update procedure: part of the Hessian is calculated explicitly and only the part that relates to the second derivatives of the dynamics is estimated using a Hessian update. The proposed method shows a large improvement in computational efficiency for a semi-large-scale poly-ethylene reactor NMPC problem with 27 states and 6 inputs with 15 parameters each.