Adaptive control for nonlinear compartmental dynamical systems with applications to clinical pharmacology

There are significant potential clinical applications of adaptive control for pharmacology in general, and anesthesia and critical care unit medicine in particular. Specifically, monitoring and controlling the levels of consciousness in surgery are of particular importance. Nonnegative and compartmental models provide a broad framework for biological and physiological systems, including clinical pharmacology, and are well suited for developing models for closed-loop control of drug administration. In this paper, we develop a direct adaptive control framework for nonlinear uncertain nonnegative and compartmental systems with nonnegative control inputs. The proposed framework is Lyapunov-based and guarantees partial asymptotic set-point regulation, that is, asymptotic set-point regulation with respect to part of the closed-loop system states associated with the plant. In addition, the adaptive controller guarantees that the physical system states remain in the nonnegative orthant of the state space. Finally, a numerical example involving the infusion of the anesthetic drug propofol for maintaining a desired constant level of consciousness for noncardiac surgery is provided to demonstrate implementation of the proposed approach.