Discontinuous Modeling Formulations for the Optimal Control of Partial Shutdowns*

A control strategy is proposed for the optimal operation of multi-unit system undergoing a partial shutdown. The strategy entails manipulating the degrees-of-freedom available during and after a shutdown such that production is restored in a cost-optimal fashion while meeting safety and operational constraints. In this work, we propose several efficient modeling formulations for handling model discontinuities such as shutdown thresholds, induced shutdowns and minimum shutdown duration. The problem is cast as a mixed-integer dynamic optimization problem (MIDO) and is embedded within a feedback control framework based on model predictive control (MPC). A two-tiered regularization approach is presented.