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

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 L 2 disturbances, 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.

A semi‐adaptive control approach to closed‐loop medication infusion

“…Thus, the doseresponse system (9) with the adaptive control law (11) and (22) is globally stable, and the signals e ", e a r , and e a y are bounded. Hence, P V D 0, and according to (23), e.t/ D 0 and ".t / D 0. This in turn means that R V is also bounded, and as a consequence, P V is uniformly continuous.…”

“…Early efforts focused on non-adaptive control approaches [14][15][16][17][18][19][20]. These controllers are largely built upon 241 black box [21] and classical pharmacokineticpharmacodynamic (PKPD) [22][23][24][25][26] models. More recently, efforts have been made on model-based adaptive anesthesia control.…”

“…Although suggested to be robust, these controllers have usually been tested in limited subject populations and would be susceptible to uncertainties because of the large inter-individual variability were they to be tested over a wide range of diverse subjects. Because of these challenges, existing work based on PKPD models has employed techniques such as linearizing the Hill equation [23], fixing either PK or PD model while adapting the other [24,25] using nonlinear filtering techniques (such as the extended Kalman filter) to adapt the nonlinear Hill equation while constraining the PKPD model to reduce the number of parameters to be tuned [26]. These controllers are largely built upon 241 black box [21] and classical pharmacokineticpharmacodynamic (PKPD) [22][23][24][25][26] models.…”

“…Closed-loop control of total intravenous anesthesia, sedation, and analgesia has been an active area of research for a few decades [14][15][16][17][18][19][20][21][22][23][24][25][26]. Early efforts focused on non-adaptive control approaches [14][15][16][17][18][19][20].…”

“…More recently, efforts have been made on model-based adaptive anesthesia control. These controllers are largely built upon 241 black box [21] and classical pharmacokineticpharmacodynamic (PKPD) [22][23][24][25][26] models. The main challenge associated with the black-box models is model structure selection: not much consensus has been established as to the best black-box model or even as to the universal efficacy of a particular black-box model structure in wide-ranging subject populations.…”