Dynamic Optimization under Uncertainty via NCO Tracking: A Solution Model Approach

The use of measurements to compensate the effect of uncertainty has recently gained attention in the context of optimization of dynamic systems. In this field, termed measurement-based optimization, two main categories can be distinguished depending on whether a model of the process or a model of the solution is used for processing the measurements. The former has been studied extensively in the literature, while tracking of the Necessary Conditions of Optimality (NCO tracking) recently proposed by the authors falls in the latter category. In this paper, the NCO-tracking scheme is viewed from the perspective of a model of the solution. The fixed part of the solution model is the one not affected by uncertainty, while the free part includes scalars and time functions that typically change with uncertainty. The variables of the free part are assigned to constraints and sensitivities, both during the run and at terminal time, resulting in a “color coding” of all input elements. Optimization is then performed by adjusting the free variables using measurements. NCO tracking using solution models is demonstrated on a simple illustrative reactor example.