A mixed chemotherapy–immunotherapy treatment protocol is developed for cancer treatment. Chemotherapy pushes the trajectory of the system towards the desired equilibrium point, and then immunotherapy alters the dynamics of the system by affecting the parameters of the system. A co-existing cancerous equilibrium point is considered as the desired equilibrium point instead of the tumour-free equilibrium. Chemotherapy protocol is derived using the pseudo-spectral (PS) controller due to its high convergence rate and simple implementation structure. Thus, one of the contributions of this study is simplifying the design procedure and reducing the controller computational load in comparison with Lyapunov-based controllers. In this method, an infinite-horizon optimal control problem is proposed for a non-linear cancer model. Then, the infinite-horizon optimal control of cancer is transformed into a non-linear programming problem. The efficient Legendre PS scheme is suggested to solve the proposed problem. Then, the dynamics of the system is modified by immunotherapy is another contribution. To restrict the upper limit of the chemo-drug dose based on the age of the patients, a Mamdani fuzzy system is designed, which is not present yet. Simulation results on four different dynamics cases how the efficiency of the proposed treatment strategy.

中文翻译：

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控制癌症药物剂量的伪光谱方法


为癌症治疗制定了混合化疗-免疫疗法治疗方案。化疗将系统的轨迹推向所需的平衡点，然后免疫疗法通过影响系统的参数来改变系统的动力学。共存的癌性平衡点被认为是所需的平衡点，而不是无肿瘤平衡点。化疗协议是使用伪谱（PS）控制器导出的，因为它具有高收敛速度和简单的实现结构。因此，与基于李雅普诺夫的控制器相比，本研究的贡献之一是简化了设计过程并减少了控制器的计算负载。在该方法中，针对非线性癌症模型提出了无限范围最优控制问题。然后，癌症的无限视野最优控制转化为非线性规划问题。建议采用高效的 Legendre PS 方案来解决所提出的问题。然后，通过免疫疗法改变系统的动力学是另一个贡献。为了根据患者的年龄限制化疗药物剂量的上限，设计了一种目前尚不存在的Mamdani模糊系统。四种不同动态情况下的仿真结果表明所提出的处理策略的效率如何。