Here, a model-free controller for cancer treatment is presented. The treatment objective is to find a proper drug dosage that can reduce the population of tumour cells. Recently, some solutions have been proposed according to the control theory. In these approaches, based on the mathematical description of the number of effector cells, tumour cells, and concentration of the interleukin-2 (IL-2), a non-linear controller is designed. Here, based on the back-stepping design procedure and function approximation property of Legendre polynomials, a novel controller for MIMO cancer immunotherapy is presented. In fact, Legendre polynomials play the role of uncertainty estimation and compensation. In comparison with other uncertainty estimators such as neural networks, Legendre polynomials have simpler structure. Thus, the contribution of this study is simplifying the design procedure and reducing the controller computational load in comparison with Neuro-Fuzzy controllers. The resulting closed-loop system is capable of overcoming various uncertainties. Simulation results verify the efficiency of the proposed method in the fast reduction of tumour cells. Moreover, a comparison between the performance of Legendre polynomials and a radial basis functions neural network (RBFN) is presented.

中文翻译：

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使用勒让德多项式的自适应后退癌症控制。

在这里，介绍了一种用于癌症治疗的无模型控制器。治疗目标是找到可以减少肿瘤细胞数量的适当药物剂量。最近，已经根据控制理论提出了一些解决方案。在这些方法中，基于效应细胞、肿瘤细胞的数量和白细胞介素 2 (IL-2) 浓度的数学描述，设计了一个非线性控制器。在这里，基于勒让德多项式的反步设计过程和函数逼近特性，提出了一种用于 MIMO 癌症免疫治疗的新型控制器。事实上，勒让德多项式起到了不确定性估计和补偿的作用。与神经网络等其他不确定性估计器相比，勒让德多项式具有更简单的结构。因此，与 Neuro-Fuzzy 控制器相比，这项研究的贡献在于简化了设计程序并减少了控制器的计算负荷。由此产生的闭环系统能够克服各种不确定性。仿真结果验证了所提方法在快速减少肿瘤细胞方面的有效性。此外，还比较了勒让德多项式和径向基函数神经网络 (RBFN) 的性能。