Implementation and acceleration of optimal control for systems biology

Area of Science:

• Computational Biology
• Control Theory
• Applied Mathematics

Background:

• Optimal control theory aids resource allocation decisions.
• Forward-backward sweep method (FBSM) solves two-point boundary value problems from Pontryagin's maximum principle (PMP).
• FBSM is widely used in systems biology due to its scalability and ease of implementation.

Purpose of the Study:

• To review the Pontryagin's maximum principle (PMP) approach and FBSM implementation.
• To enhance FBSM convergence rates by adapting existing acceleration techniques.
• To demonstrate improved convergence without extensive parameter tuning.

Main Methods:

• Conceptualizing FBSM as a fixed-point iteration process.
• Leveraging and adapting existing acceleration techniques for iterative methods.
• Implementing and testing accelerated FBSM on relevant problems.

Main Results:

• Convergence improvement was achieved without costly tuning.
• Adapted acceleration techniques enhanced FBSM convergence rates.
• Methods induced convergence in cases where standard FBSM failed.

Conclusions:

• Accelerated FBSM offers improved performance and reliability for optimal control problems.
• This approach enhances the applicability of FBSM in systems biology and other fields.
• The presented methods provide a practical way to improve convergence for complex systems.