In practice, many physical systems, including physiological ones, can be considered whose input can take only positive quantities. However, most of the conventional control methods do not support the positivity of the main input data to the system. Furthermore, the parameters of these systems, similar to other non-linear systems, are either not accurately identified or may change over time. Therefore, it is reasonable to design a controller that is robust against system uncertainties. A robust positive-input control method is proposed for the automatic treatment of targeted anti-angiogenic therapy implementing a recently published tumour growth model based on experiments conducted on mouse models. The backstepping (BS) approach is applied to design the positive input controller using sensory data of tumour volume as feedback. Unlike previous studies, the proposed controller only requires the measurement of tumour volume and does not require the measurement of inhibitor level. The exponential stability of the controlled system is proved mathematically using the Lyapunov theorem. As a result, the convergence rate of the tumour volume can be controlled, which is an important issue in cancer treatment. Moreover, the robustness of the system against parametric uncertainties is verified mathematically using the Lyapunov theorem. The real-time simulation results-based (OPAL-RT) and comparisons with previous studies confirm the theoretical findings and effectiveness of the proposed method.

中文翻译：

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使用血管生成抑制对肿瘤生长进行强有力的正向控制。

在实践中，许多物理系统，包括生理系统，可以被认为其输入只能取正数。然而，大多数常规控制方法不支持系统主要输入数据的积极性。此外，与其他非线性系统类似，这些系统的参数要么无法准确识别，要么可能随时间而变化。因此，设计一个对系统不确定性具有鲁棒性的控制器是合理的。提出了一种鲁棒的正输入控制方法，用于自动治疗靶向抗血管生成疗法，实施基于小鼠模型实验的最近发表的肿瘤生长模型。应用反步（BS）方法来设计正输入控制器，使用肿瘤体积的感觉数据作为反馈。与之前的研究不同，所提出的控制器只需要测量肿瘤体积，不需要测量抑制剂水平。利用李雅普诺夫定理在数学上证明了受控系统的指数稳定性。因此，可以控制肿瘤体积的收敛速度，这是癌症治疗中的一个重要问题。此外，系统针对参数不确定性的鲁棒性通过李雅普诺夫定理进行了数学验证。基于实时仿真结果（OPAL-RT）以及与先前研究的比较证实了该方法的理论发现和有效性。