Simulation-Based Approach for Optimal Control of a Stefan Problem

This article describes a technique for solving optimal control problems by transformation into a system of differential-algebraic equations (DAEs). The optimal control vector can be obtained via simulation of the resulting DAE system with the selected DAE solver, eliminating the need for an optimization solver. This simulation-based (DAE-based) technique is demonstrated and benchmarked against various optimization-based approaches via two case studies associated with optimization and control of a Stefan problem. Results show that the simulation-based approach is faster than every optimization-based method by more than an order of magnitude while giving accurate solutions in all cases. The proposed framework offers a promising alternative to the traditional techniques in optimal control-related applications where speed is crucial, e.g., real-time online model predictive control.