Robust dynamic optimization of batch processes under parametric uncertainty: Utilizing approaches from semi-infinite programs

The optimal solution in dynamic optimization of batch processes often exhibits active path constraints. The goal of this work is the robust satisfaction of path constraints in the presence of parametric uncertainties based on known worst-case formulations. These formulations are interpreted as semi-infinite programs (SIP). Two known SIP algorithms are extended to the dynamic case and assessed. One is a discretization approach and the other a local reduction approach. With these presented concepts, robust path constraint satisfaction is in principle guaranteed. In this work, however, local methods are used to approximate the global solution of the lower-level problem with local solvers thus allowing for (rather unlikely) constraint violations. Finally, the penicillin fermentation is introduced as a well-known case study with uncertainties, which is modified in this work by adding further dependencies. The adaptation of the SIP concepts to dynamic optimization problems are shown to be successful for this case study.