Adaptive Control of Mammillary Drug Delivery Systems with Actuator Amplitude Constraints and System Time Delays

In this paper, we develop a direct adaptive control framework for uncertain linear compartmental dynamical systems with actuator amplitude constraints and system time delays. The specific focus of the paper is on compartmental pharmacokinetic models and their applications to drug delivery systems. In particular, we develop a Lyapunov-Krasovskii-based direct adaptive control framework for guaranteeing set-point regulation of the closed-loop system in the nonnegative orthant in the presence of unknown system time delays and control amplitude constraints. The framework additionally guarantees nonnegativity of the control signal. Finally, a numerical example involving the infusion of the anesthetic drug propofol for maintaining a desired constant level of depth of anesthesia for noncardiac surgery is provided to demonstrate the framework on a drug delivery mammillary model for general anesthesia involving system time delays and control infusion rate constraints.