In Diabetes Mellitus, the pancreas remains incapable of insulin administration that leads to hyperglycaemia, an escalated glycaemic concentration, which may stimulate many complications. To circumvent this situation, a closed-loop control strategy is much needed for the exogenous insulin infusion in diabetic patients. This closed-loop structure is often termed as an artificial pancreas that is generally established by the employment of different feedback control strategies. In this work, the authors have proposed an arbitrary-order sliding mode control approach for development of the said mechanism. The term, arbitrary, is exercised in the sense of its applicability to any n-order controllable canonical system. The proposed control algorithm affirms the finite-time effective stabilisation of the glucose-insulin regulatory system, at the desired level, with the alleviation of sharp fluctuations. The novelty of this work lies in the sliding manifold that incorporates indirect non-linear terms. In addition, the necessary discontinuous terms are filtered-out once before its employment to the plant, i.e. diabetic patient. The robustness, in the presence of external disturbances, i.e. meal intake is confirmed via rigorous mathematical stability analysis. In addition, the effectiveness of the proposed control strategy is ascertained by comparing the results with the standard literature.

中文翻译：

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用于开发人工胰腺机构的基于任意阶滑模的鲁棒控制算法。

在糖尿病中，胰腺仍然无法注射胰岛素，从而导致高血糖，血糖浓度升高，这可能会引发许多并发症。为了避免这种情况，糖尿病患者的外源性胰岛素输注非常需要闭环控制策略。这种闭环结构通常被称为人工胰腺，通常是通过采用不同的反馈控制策略来建立的。在这项工作中，作者提出了一种任意阶滑模控制方法来开发上述机制。术语“任意”是在其适用于任何 n 阶可控规范系统的意义上使用的。所提出的控制算法确认了葡萄糖-胰岛素调节系统在所需水平上的有限时间有效稳定，并减轻了急剧波动。这项工作的新颖之处在于包含间接非线性项的滑动流形。此外，必要的不连续项在其被应用到设备（即糖尿病患者）之前被过滤掉一次。在存在外部干扰（即膳食摄入）的情况下，鲁棒性通过严格的数学稳定性分析来确认。此外，通过将结果与标准文献进行比较，确定了所提出的控制策略的有效性。