Tracking the Necessary Conditions of Optimality

Eric Visser, FRANCOIS Gregory, WELZ Carsten, SRINIVASAN Bala, BONVIN Dominique

Dynamic optimization has been widely studied in literature. The available studies often involve implementing a profile that has been determined off-line on the basis of a model. However, this approach may not lead to optimality when there is uncertainty on raw materials, model parameters, or when there are some disturbances. Industry typically copes with uncertainty by introducing conservatism that guarantees constraint satisfaction. Such an approach is normally very conservative and performance can be quite poor. The core idea of measurement-based optimization is to use process measurements to compensate for the effect of uncertainty.

Among measurement-based optimization methods, the indirect ones are those where the model is refined periodically and used for reoptimization. This method is computationally expensive and the model-refinement suffers from the lack of persistency of excitation. Thus, the direct measurement-based optimization approach is investigated here, where an optimized reference is tracked.

The main contribution of this project is to demonstrate that the necessary conditions of optimality can be tracked in the presence of uncertainty. The optimal solution consists of two parts, (i) the constraints and (ii) the sensitivities, i.e, the gradient of the cost with respect to the input. Furthermore, in dynamic optimization, there are two types of constraints and sensitivity conditions: i) the path conditions that are related to quantities during the batch and ii) the terminal conditions that are related to quantities at the end of the batch. Various methodologies for tracking the path and terminal conditions using appropriate measurements are considered in subsequent projects.

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