A mathematical model for the robust blood glucose tracking

Weijiu Liu; Weijiu Liu

doi:10.3934/mbe.2019036

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 2: 759-781. doi: 10.3934/mbe.2019036

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Research article

A mathematical model for the robust blood glucose tracking

Weijiu Liu ^,

Department of Mathematics, University of Central Arkansas, 201 Donaghey Avenue, Conway, AR 72035, USA

Received: 20 August 2018 Accepted: 23 November 2018 Published: 15 January 2019

In this paper, we study the problem of the robust blood glucose tracking. Tracking here means that the error between a state variable of a system under control and its desired time-varying reference converges to zero over time. Robustness here means that a controller designed for a system can tolerate a small variation of the system parameters. Since the parameters in the blood glucose regulation system differ in people, such a robust controller is useful in the insulin pump technology: an insulin pump equipped with such a robust controller could be used in a group of people. Thus, in our study, parameter uncertainties are introduced into a mathematical model of the blood glucose regulation system. Using an actual blood glucose level as feedback and an exogenous glucose input and a desired glucose reference as feedforward, we design a robust feedback and feedforward controller, which drives the blood glucose to track the desired time-varying glucose reference for any small uncertainties. Numerical simulations with published experimental blood glucose data are conducted to further confirm our theoretical results.
- diabetes,
- robust blood glucose tracking,
- feedback and feedforward control,
- parameter uncertainty,
- internal model
Citation: Weijiu Liu. A mathematical model for the robust blood glucose tracking[J]. Mathematical Biosciences and Engineering, 2019, 16(2): 759-781. doi: 10.3934/mbe.2019036

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Abstract

In this paper, we study the problem of the robust blood glucose tracking. Tracking here means that the error between a state variable of a system under control and its desired time-varying reference converges to zero over time. Robustness here means that a controller designed for a system can tolerate a small variation of the system parameters. Since the parameters in the blood glucose regulation system differ in people, such a robust controller is useful in the insulin pump technology: an insulin pump equipped with such a robust controller could be used in a group of people. Thus, in our study, parameter uncertainties are introduced into a mathematical model of the blood glucose regulation system. Using an actual blood glucose level as feedback and an exogenous glucose input and a desired glucose reference as feedforward, we design a robust feedback and feedforward controller, which drives the blood glucose to track the desired time-varying glucose reference for any small uncertainties. Numerical simulations with published experimental blood glucose data are conducted to further confirm our theoretical results.

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