Highly Efficient Optimal Control for Lyophilization via Simulation of Discrete/Continuous Mixed-index Differential-algebraic Equations

This article presents a highly efficient optimal control algorithm and policies for lyophilization (also known as freeze drying). The optimal solutions and control policies are derived using an extended version of the simulation-based algorithm, which reformulates the optimal control problem as a hybrid discrete/continuous system of mixed-index differential-algebraic equations and subsequently calculates the optimal control vector via simulation of the resulting DAEs. Our algorithm and control policies are demonstrated via a number of case studies that encompass various lyophilization and optimal control strategies. All the case studies can be solved within less than a second on a normal laptop, regardless of their complexity. The method is several orders of magnitude faster than the traditional optimization-based techniques while giving similar/better accuracy. The proposed algorithm offers an efficient and reliable framework for optimal control of lyophilization, which can also be extended to other similar systems with phase transitions.