Asymptotic tracking and disturbance rejection of the blood glucose regulation system

• Published in: Mathematical biosciences Vol. 289; pp. 78 - 88
• Main Authors: Ashley, Brandon, Liu, Weijiu
• Format: Journal Article
• Language: English
• Published: United States Elsevier Inc 01.07.2017; Elsevier Science Ltd
• Subjects: Algorithms; Asymptotic methods; Asymptotic properties; Asymptotic tracking; Blood; Blood glucose; Blood Glucose - metabolism; Center manifold theory; Computer simulation; Control; Control systems; Control theory; Diabetes; Diabetes mellitus; Diabetes mellitus (insulin dependent); Diabetes Mellitus, Type 1 - metabolism; Differential equations; Disturbance rejection; Disturbances; Eigenvalues; Feedback; Feedforward control; Glucose; Glucose monitoring; Glucose regulation; Humans; Insulin; Insulin - metabolism; Insulin Infusion Systems; Mathematical models; Models, Biological; Nonlinear differential equations; Nonlinear equations; Pancreas; Pancreas, Artificial; Partial differential equations; Tracking; Glucose regulation; Center manifold theory; Disturbance rejection; Diabetes; Asymptotic tracking
• ISSN: 0025-5564; 1879-3134; 1879-3134
• DOI: 10.1016/j.mbs.2017.05.001

•Mathematical modeling of the blood glucose regulation system subject to an exogenous glucose disturbance.•Mathematical modeling of an exogenous glucose disturbance.•Using the center manifold theory to establish blood glucose regulator equations and then using their solutions to synthesize feedback and feedforward controllers to reject the blood glucose disturbance and asymptotically track a constant glucose reference of 90 mg/dl.•Linear approximate solutions of the blood glucose regulator equations. Type 1 diabetes patients need external insulin to maintain blood glucose within a narrow range from 65 to 108 mg/dl (3.6 to 6.0 mmol/l). A mathematical model for the blood glucose regulation is required for integrating a glucose monitoring system into insulin pump technology to form a closed-loop insulin delivery system on the feedback of the blood glucose, the so-called “artificial pancreas”. The objective of this paper is to treat the exogenous glucose from food as a glucose disturbance and then develop a closed-loop feedback and feedforward control system for the blood glucose regulation system subject to the exogenous glucose disturbance. For this, a mathematical model for the glucose disturbance is proposed on the basis of experimental data, and then incorporated into an existing blood glucose regulation model. Because all the eigenvalues of the disturbance model have zero real parts, the center manifold theory is used to establish blood glucose regulator equations. We then use their solutions to synthesize a required feedback and feedforward controller to reject the disturbance and asymptotically track a constant glucose reference of 90  mg/dl. Since the regulator equations are nonlinear partial differential equations and usually impossible to solve analytically, a linear approximation solution is obtained. Our numerical simulations show that, under the linear approximate feedback and feedforward controller, the blood glucose asymptotically tracks its desired level of 90 mg/dl approximately.