Department of Mathematics, University of Central Arkansas, 201 Donaghey Avenue, Conway, AR 72035, USA.
Math Biosci Eng. 2019 Jan 15;16(2):759-781. doi: 10.3934/mbe.2019036.
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.
本文研究了鲁棒血糖跟踪问题。这里的跟踪是指被控系统的状态变量与其期望时变参考之间的误差随时间收敛到零。这里的鲁棒性是指为系统设计的控制器能够容忍系统参数的小变化。由于血糖调节系统中的参数因人而异，因此这种鲁棒控制器在胰岛素泵技术中很有用：配备这种鲁棒控制器的胰岛素泵可以在一组人群中使用。因此，在我们的研究中，将参数不确定性引入到血糖调节系统的数学模型中。使用实际血糖水平作为反馈，外加葡萄糖输入和期望血糖参考作为前馈，我们设计了一个鲁棒的反馈和前馈控制器，该控制器可以使血糖跟踪任何小不确定性的期望时变血糖参考。使用已发表的实验血糖数据进行数值模拟，进一步证实了我们的理论结果。
