In this article, the optimal control strategy for organism is investigated by using the adaptive dynamic programming (ADP) method under the architecture of nonzero-sum games (NZSGs). First, a tumor model is established to formulate the interaction relationships among normal cells, tumor cells, endothelial cells, and the concentrations of drugs. Then, the ADP-based method of single-critic network architecture is proposed to approximate the coupled Hamilton_Jacobi equations (HJEs) under the medicine dosage regulation mechanism (MDRM). According to the game theory, the approximate MDRM-based optimal strategy can be derived, which is of great practical significance. Owing to the proposed mechanism, the dosages of the chemotherapy and anti-angiogenic drugs can be regulated timely and necessarily. Furthermore, the stability of the closed-loop system with the obtained strategy is analyzed via the Lyapunov theory. Finally, a simulation experiment is conducted to verify the effectiveness of the proposed method.

中文翻译：

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利用药物剂量调节机制对生物体进行基于联合治疗的自适应控制


本文利用非零和博弈（NZSGs）架构下的自适应动态规划（ADP）方法研究了生物体的最优控制策略。首先，建立肿瘤模型来制定正常细胞、肿瘤细胞、内皮细胞和药物浓度之间的相互作用关系。然后，提出基于ADP的单批评网络架构方法来近似药物剂量调节机制（MDRM）下的耦合Hamilton_Jacobi方程（HJE）。根据博弈论，可以推导出基于MDRM的近似最优策略，具有重要的现实意义。由于所提出的机制，可以及时、必要地调节化疗和抗血管生成药物的剂量。此外，通过李亚普诺夫理论分析了采用所获得策略的闭环系统的稳定性。最后进行仿真实验验证所提方法的有效性。