Implementation and acceleration of optimal control for systems biology

Optimal control theory provides insight into complex resource allocation decisions. The forward-backward sweep method (FBSM) is an iterative technique commonly implemented to solve two-point boundary value problems arising from the application of Pontryagin's maximum principle (PMP) in optimal control. The FBSM is popular in systems biology as it scales well with system size and is straightforward to implement. In this review, we discuss the PMP approach to optimal control and the implementation of the FBSM. By conceptualizing the FBSM as a fixed point iteration process, we leverage and adapt existing acceleration techniques to improve its rate of convergence. We show that convergence improvement is attainable without prohibitively costly tuning of the acceleration techniques. Furthermore, we demonstrate that these methods can induce convergence where the underlying FBSM fails to converge. All code used in this work to implement the FBSM and acceleration techniques is available on GitHub at https://github.com/Jesse-Sharp/Sharp2021.

Automated summary

This review discusses the application of Pontryagin's maximum principle (PMP) in optimal control and the implementation of the forward-backward sweep method (FBSM). By conceptualizing FBSM as a fixed point iteration process and adapting existing acceleration techniques, the rate of convergence can be improved without costly tuning. Moreover, these methods can induce convergence in cases where the FBSM fails to converge.