Adaptive disturbance rejection control for compartmental systems with application to intraoperative anesthesia influenced by hemorrhage and hemodilution effects

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Abstract
Compartmental system models involve dynamic states whose values are nonnegative. 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 disturbance rejection control framework for compartmental dynamical systems with exogenous bounded disturbances. The proposed framework is Lyapunov based and guarantees partial asymptotic stability of the closed‐loop system, that is, asymptotic stability with respect to part of the closed‐loop system states associated with the plant dynamics. The remainder of the states associated with the adaptive controller gains are shown to be Lyapunov stable. In the case of bounded energy ℒ︁2disturbances, the proposed approach guarantees a nonexpansivity constraint on the closed‐loop input–output map between the plant disturbances and performance variables. Finally, a numerical example involving the infusion of the anesthetic drug propofol for maintaining a desired constant level of depth of anesthesia for surgery in the face of continuing hemorrhage and hemodilution is provided. Copyright © 2008 John Wiley & Sons, Ltd.

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