Optimization problems in chemical engineering often involve complex systems of nonlinear DAE as the model equations. The direct multiple shooting method has been known for a while as a fast off-line method for optimization problems in ODE and later in DAE. Some factors crucial for its fast performance are briefly reviewed. The direct multiple shooting approach has been successfully adapted to the specific requirements of real-time optimization. Special strategies have been developed to effectively minimize the on-line computational effort, in which the progress of the optimization iterations is nested with the progress of the process. They use precalculated information as far as possible (e.g. Hessians, gradients and QP presolves for iterated reference trajectories) to minimize response time in case of perturbations. In typical real-time problems they have proven much faster than fast off-line strategies. Compared with an optimal feedback control computable upper bounds for the loss of optimality can be established that are small in practice. Numerical results for the Nonlinear Model Predictive Control (NMPC) of a high-purity distillation column subject to parameter disturbances are presented.

Real-time optimization and nonlinear model predictive control of processes governed by differential-algebraic equations