Multiple-time-delay H $$_\infty$$ controller synthesis for glycemic regulation of a hybrid diabetes system

IF 1.9 4区 数学 Q1 MATHEMATICS
S. Syafiie
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引用次数: 0

Abstract

A mathematical model is used to represent a physical system. To mimic closely to a real system, the mathematical model may present in functional differential equations. Most of the processes exhibit multiple time-varying delayed phenomena. This paper aims to develop a memory-less controller that achieves H\(_\infty\) performance for disturbance rejection. The proposed technique for controller design ensures closed-loop stability of a chosen Lyapunov-Krasovskii functional (LKF). while, the integral functions derived from the LKF’s derivative are addressed through the utilization of free matrix inequality The development of stability condition is presented in linear matrix inequality. Based on the developed stability condition, the optimal controller gain is obtained after minimization of the H\(_\infty\) performance. The proposed controller design technique is simulated to stabilize a diabetes system upon periodic glucose absorption as a disturbance function. Clearly, the controller is able to regulate insulin maintaining the blood glucose concentration to the healthy patient concentration upon introducing meal ingestion as periodic disturbances. Compare to an existing method, the proposed controller has lower peak in the rejecting the introducing disturbances.

Abstract Image

用于混合糖尿病系统血糖调节的多时延 H $$_infty$ 控制器合成
数学模型用于表示物理系统。为了接近真实系统,数学模型可以用函数微分方程来表示。大多数过程都表现出多种时变延迟现象。本文旨在开发一种无内存控制器,它能实现 H\(_\infty\) 性能的干扰抑制。所提出的控制器设计技术确保了所选 Lyapunov-Krasovskii 函数(LKF)的闭环稳定性,同时通过利用自由矩阵不等式解决了从 LKF 的导数导出的积分函数。根据所制定的稳定性条件,在最小化 H\(_\infty\) 性能后得到了最佳控制器增益。我们对所提出的控制器设计技术进行了仿真,以稳定周期性吸收葡萄糖作为干扰函数的糖尿病系统。很明显,当引入进餐作为周期性干扰时,控制器能够调节胰岛素,使血糖浓度保持在健康患者的水平。与现有方法相比,所提出的控制器在拒绝引入干扰时具有更低的峰值。
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来源期刊
CiteScore
4.20
自引率
5.00%
发文量
44
期刊介绍: Mathematical Sciences is an international journal publishing high quality peer-reviewed original research articles that demonstrate the interaction between various disciplines of theoretical and applied mathematics. Subject areas include numerical analysis, numerical statistics, optimization, operational research, signal analysis, wavelets, image processing, fuzzy sets, spline, stochastic analysis, integral equation, differential equation, partial differential equation and combinations of the above.
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