There are numerous mathematical models simulating the behaviour of cancer by considering variety of states in different treatment strategies, such as chemotherapy. Among the models, one is developed which is able to consider the blood vessel-production (angiogenesis) in the vicinity of the tumour and the effect of anti-angiogenic therapy. In the mentioned-model, normal cells, cancer cells, endothelial cells, chemotherapy and anti-angiogenic agents are taking into account as state variables, and the rate of injection of the last two are considered as control inputs. Since controlling the cancerous tumour growth is a challenging matter for patient's life, the time schedule design of drug injection is very significant. Two optimal control strategies, an open-loop (calculus of variations) and a closed-loop (state-dependent Riccati equation), are applied on the system in order to find an optimal time scheduling for each drug injection. By defining a proper cost function, an optimal control signal is designed for each one. Both obtained control inputs have reasonable answers, and the system is controlled eventually, but by comparing them, it is concluded that both methods have their own benefits which will be discussed in details in the conclusion section.

中文翻译：

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通过抗血管生成疗法和化学疗法在癌性肿瘤中的药物递送的最佳控制方法。

有许多数学模型通过考虑不同治疗策略（例如化学疗法）中的各种状态来模拟癌症的行为。在这些模型中，开发了一种能够考虑肿瘤附近的血管生成（血管生成）和抗血管生成疗法的效果的模型。在提到的模型中，正常细胞、癌细胞、内皮细胞、化学疗法和抗血管生成剂作为状态变量被考虑在内，最后两种的注射速率被认为是控制输入。由于控制癌性肿瘤的生长对患者的生命具有挑战性，因此药物注射的时间表设计非常重要。两种最优控制策略，一个开环（变分法）和一个闭环（状态相关的 Riccati 方程），在系统上应用，以便为每次药物注射找到最佳时间安排。通过定义适当的成本函数，为每个成本函数设计一个最优控制信号。两种获得的控制输入都有合理的答案，系统最终得到控制，但是通过比较它们，可以得出结论，两种方法都有其自身的优点，这将在结论部分详细讨论。