Simulation-based Approach for Fast Optimal Control of a Stefan Problem with Application to Cell Therapy

TL;DR

This paper introduces a simulation-based method for solving optimal control problems by reformulating them as differential-algebraic equations, significantly speeding up computation while maintaining accuracy, especially useful for real-time applications.

Contribution

The paper presents a novel simulation-based approach that bypasses traditional optimization solvers for optimal control, demonstrating superior speed and comparable accuracy.

Findings

Faster than optimization-based methods by over ten times

Maintains similar or better accuracy in control solutions

Guarantees optimality if certain constraints remain active

Abstract

This article describes a new, efficient way of finding control and state trajectories in optimal control problems by reformulation as a system of differential-algebraic equations (DAEs). The optimal control and state vectors can be obtained via simulation of the resulting DAE system with the selected DAE solver, eliminating the need for an optimization solver. Our simulation-based approach is demonstrated and benchmarked against various optimization-based algorithms via four case studies associated with the optimization and control of a Stefan problem for cell therapy. The simulation-based approach is faster than every optimization-based method by more than an order of magnitude while giving similar/better accuracy in all cases. The solution obtained from the simulation-based approach is guaranteed to be optimal provided that at least one constraint or algebraic equation resulting from the reformulation remains active at all times. The proposed technique offers an efficient and reliable framework for optimal control, serving as a promising alternative to the traditional techniques in applications where speed is crucial, e.g., real-time online model predictive control.