Robust multi-objective dynamic optimization of chemical processes using the Sigma Point method

Dynamic optimization solutions largely rely on the accuracy of the underlying mathematical models. However, these models only represent an approximation of the real dynamic process and their predictions are dependent on a set of parameter values. These parameter values can be hard to estimate exactly (e.g., thermal conductivity) or vary over time (e.g., due to fouling) potentially leading to hazardous situations when applying a model based optimal solution. Robust dynamic optimization deals with the uncertainty related to these parameters in order to quantify their effect and deliver safer (i.e., more robust) operating conditions. This paper discusses a computationally efficient robust dynamic optimization approach based on the Sigma Point method and shows how it outperforms a linearization-based method for a nonlinear dynamic chemical vapor deposition reactor case-study with multiple uncertainties. Moreover, by accounting for uncertainty a trade-off between process safety and performance of the reactor is introduced. This aspect is cast in a multi-objective dynamic optimization framework. In particular, it is illustrated how an increasing robustness (i.e., process safety) induces a worsening of other investigated objective functions and results in robustified Pareto sets.