Control theory arises in most modern real-life applications, not least in biological and medical applications. In particular, in biological and medical contexts, the role of control theory began to take shape in the early 1980s when the first works appeared on the application of control theory in models of pharmacokinetics and pharmacodynamics for antitumor therapies. Forty years after those first works, the theory of control continues to be considered a mathematical analysis tool of extreme importance and usefulness, but the challenges it must overcome in order to manage the complexity of biological processes are in fact not yet overcome. In this article, we introduce the reader to the basic ideas of control theory, its aims and its mathematical formalization, and we review its use in cell phase-specific models for cancer chemotherapy. We discuss strengths and limitations of the control theory approach to the analysis pharmacokinetics and pharmacodynamics models, and we will see that most of them are strongly related to data availability and mathematical form of the model. We propose some future research directions that could prove useful in overcoming the these limitations and we indicate the crucial steps preliminary to a useful and informative application of control theory to cancer chemotherapy modeling.

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控制理论和癌症化疗：它们如何相互作用

控制理论出现在大多数现代现实生活中，尤其是在生物和医学应用中。特别是在生物学和医学背景下，控制理论的作用在 1980 年代初开始形成，当时第一部作品出现在控制理论在抗肿瘤治疗的药代动力学和药效学模型中的应用。在最初的工作四十年后，控制理论仍然被认为是一种极其重要和有用的数学分析工具，但它必须克服的挑战，以管理生物过程的复杂性，实际上尚未克服。在本文中，我们向读者介绍了控制理论的基本思想、其目标及其数学形式化，并回顾了其在癌症化疗的细胞阶段特异性模型中的应用。我们讨论了分析药代动力学和药效学模型的控制理论方法的优点和局限性，我们将看到它们中的大多数与模型的数据可用性和数学形式密切相关。我们提出了一些未来的研究方向，这些方向可能被证明有助于克服这些局限性，并且我们指出了控制理论在癌症化疗建模中有用且信息丰富的应用的关键步骤。