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A mathematical model for the robust blood glucose tracking

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

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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Keywords 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. Mathematical Biosciences and Engineering, 2019, 16(2): 759-781. doi: 10.3934/mbe.2019036

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