Department of Mathematics,Faculty of Science and Technology, Universitas Airlangga, Surabaya, Indonesia; Department of Computer Science and Mathematics, Lebanese American University, 1107-2020, Beirut, Lebanon.
Department of Mathematics and Statistics, The University of Lahore, Pakistan.
Comput Methods Programs Biomed. 2024 Dec;257:108420. doi: 10.1016/j.cmpb.2024.108420. Epub 2024 Sep 14.
In this paper, we developed a significant class of control issues regulated by nonlinear fractal order systems with input and output signals, our goal is to design a direct transcription method with impulsive instant order. Recent advances in the artificial pancreas system provide an emerging treatment option for type 1 diabetes. The performance of the blood glucose regulation directly relies on the accuracy of the glucose-insulin modeling. This work leads to the monitoring and assessment of comprehensive type-1 diabetes mellitus for controller design of artificial panaceas for the precision of the glucose-insulin glucagon in finite time with Caputo fractional approach for three primary subsystems.
For the proposed model, we admire the qualitative analysis with equilibrium points lying in the feasible region. Model satisfied the biological feasibility with the Lipschitz criteria and linear growth is examined, considering positive solutions, boundedness and uniqueness at equilibrium points with Leray-Schauder results under time scale ideas. Within each subsystem, the virtual control input laws are derived by the application of input to state theorems and Ulam Hyers Rassias.
Chaotic Relation of Glucose insulin glucagon compartmental in the feasible region and stable in finite time interval monitoring is derived through simulations that are stable and bounded in the feasible regions. Additionally, as blood glucose is the only measurable state variable, the unscented power-law kernel estimator appropriately takes into account the significant problem of estimating inaccessible state variables that are bound to significant values for the glucose-insulin system. The comparative results on the simulated patients suggest that the suggested controller strategy performs remarkably better than the compared methods.
In the model under investigation, parametric uncertainties are identified since the glucose, insulin, and glucagon system's parameters are accurately measured numerically at different fractional order values. In terms of algorithm resilience and Caputo tracking in the presence of glucagon and insulin intake disturbance to maintain the glucose level. A comprehensive analysis of numerous difficult test issues is conducted in order to offer a thorough justification of the planned strategy to control the type 1 diabetes mellitus with designed the artificial pancreas.
本文研究了一类具有输入输出信号的非线性分形阶系统的控制问题，目标是设计一种具有脉冲瞬时阶的直接转录方法。人工胰腺系统的最新进展为 1 型糖尿病提供了一种新兴的治疗选择。血糖调节的性能直接依赖于血糖-胰岛素模型的准确性。这项工作导致了对 1 型糖尿病的综合监测和评估，为人工胰腺的控制器设计提供了葡萄糖-胰岛素胰高血糖素的有限时间精度，使用 Caputo 分数阶方法对三个主要子系统进行了研究。
对于所提出的模型，我们欣赏了平衡点位于可行区域内的定性分析。在时间尺度思想下，通过考虑正解、平衡点处的有界性和唯一性，利用平衡点处的 Lipschitz 准则和线性增长检验模型的生物学可行性。在每个子系统中，通过应用输入状态定理和 Ulam-Hyers-Rassias 导出了虚拟控制输入律。
通过仿真得出了在可行区域内的葡萄糖-胰岛素-胰高血糖素腔混沌关系，并在有限时间间隔内进行了稳定监测，在可行区域内是稳定有界的。此外，由于血糖是唯一可测量的状态变量，无迹幂律核估计器适当地考虑了估计无法访问的状态变量的重要问题，这些状态变量对于血糖-胰岛素系统来说必然具有重要的值。对模拟患者的比较结果表明，所提出的控制器策略的性能明显优于比较方法。
在所研究的模型中，由于葡萄糖、胰岛素和胰高血糖素系统的参数在不同分数阶值下可以精确地数值测量，因此存在参数不确定性。在存在胰高血糖素和胰岛素摄入干扰的情况下，保持血糖水平的算法弹性和 Caputo 跟踪能力。为了全面分析大量困难的测试问题，提出了一种综合控制策略，用于设计人工胰腺来控制 1 型糖尿病。
