Multi-model approach based on parametric sensitivities - A heuristic approximation for dynamic optimization of semi-batch processes with parametric uncertainties

Optimal processes often exhibit active path constraints. Parametric uncertainties in the process model might thus lead to constraint violations. A heuristic approach is presented to overcome this challenge. The nominal model is optimized with additional path constraints due to worst-case models. A heuristic method of choosing these models is proposed based on sensitivities of the constraints with respect to the uncertain parameters. The presented approximation does not guarantee robust feasibility, but path constraint violations are less likely to occur compared to the optimization using the nominal model solely. Two case studies are presented: a complex emulsion copolymerization process (DAE with 139 equations) and the penicillin formation (four differential equations and two algebraic equations). The results of both case studies show that, in contrast to the optimization in the nominal case, the multi-model approach does not violate the path constraints for different scenarios of the parametric uncertainty set.