Hamilton-Jacobi Safety Analysis (HJSA) is a framework in control engineering used to automatically design control algorithms for safety-critical systems. This methodology has become a powerful tool in robotics, reinforcement learning, and other engineering disciplines, but it remains limited in biomedical applications. In pharmacology, HJSA is in theory an ideal tool to design optimal drug treatment regimens from pharmacokinetic and pharmacodynamic (PKPD) models, as to achieve a therapeutic window without ever violating toxicity thresholds. Critically, HJSA even permits analysis of models for combination therapies, where dosing regimen design can be particularly challenging. However, the complex, multi-scale nature of PKPD models renders HJSA too slow for practical use. Additionally, the standard control tasks in HJSA are too limited for even basic optimal dosing problems. In this talk, we will give a brief overview of HJSA and the various methodologies we have designed to extend this methodology to pharmacology problems. We will conclude with an overview of the remaining work on this project, which will be dedicated to demonstrating the extended methodology on specific pharmacology problems of interest.

The video of this presentation is available here.