Direct adaptive control of nonnegative and compartmental dynamical systems with time delay

We develop a direct adaptive control framework for uncertain linear nonnegative and compartmental dynamical systems with unknown time delay. 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 delay. The framework additionally guarantees nonnegativity of the control signal. Finally, we demonstrate the framework on a drug delivery model for general anesthesia involving system time delays.