LMI-Enabled Absolutely Stabilizing PID Control of Pharmacological Systems for Closed-Loop Automated Intravenous Drug Administration

Objective: We developed a linear matrix inequality-enabled absolutely stabilizing proportional-integral-derivative control design approach for pharmacological systems applicable to intravenous drug administration. Methods: We developed a proportional-integral- derivative control design approach that does not require detailed knowledge of the dose-response relationship other than its sector bound. It repetitively solves a set of linear matrix inequalities, which encapsulate the Lyapunov stability conditions against unknown dose-response relationship, over a broad proportional-integral-derivative gain space. The linear matrix inequality-feasible proportional-integral-derivative gains guarantee the absolute stability of the closed-loop control system against unknown yet sector-bounded dose-response relationship. The proof-of-concept of the approach was shown in silico using intravenous propofol anesthesia as a practical case scenario. Results: The in silico evaluation results demonstrated the robustness and performance of the proportional-integral- derivative controllers designed with the proposed control design approach against unknown sector-bounded nonlinear dose-response relationship and parametric uncertainty in the plant dynamics. Conclusion: Pending follow-up development and extensive evaluation in various complex intravenous drug administration problems, the proposed approach may find applications in various closed-loop automated intravenous drug administration problems with complex and highly nonlinear dose-response relationships. Significance: The proposed control design approach provides a systematic way to absolutely stabilize pharmacological systems against unknown, nonlinear, and time- varying dose-response relationship, perhaps for the first time.