Adaptive control for nonnegative and compartmental dynamical systems with applications to general anesthesia

Nonnegative and compartmental dynamical system models are composed of homogeneous interconnected subsystems or compartments which exchange variable nonnegative quantities of material with conservation laws describing transfer, accumulation, and excretion between the compartments and the environment. These models are widespread in biological and physiological sciences and play a key role in understanding these processes. In this paper, we develop a direct adaptive control framework for linear uncertain nonnegative and compartmental systems. 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, the proposed approach is used to control the infusion of the anesthetic drug propofol for maintaining a desired constant level of depth of anesthesia for noncardiac surgery.