Cancer is one of the leading factors of human mortality. The main goal of this article is to present and control a tumor treatment immunity. It can adaptively benefit from the advantages of back-stepping control, the sliding mode control, fuzzy control, and parameter estimation. The cancerous tumor proposed model is a Multi-Input Multi-Output (MIMO) nonlinear fractional-order model. A new back-stepping model based on the sliding mode controller is designed in this paper to deal with the convergence velocity and achieve a robust controller. A new combined Back-Stepping controller with the approach of sliding mode has been designed to solve the convergence velocity challenge, and to face the ordinary back-stepping robustness issue of the controller. Since nonlinear expressions are considered in an indefinite model, a fuzzy controller has been applied to model them. The parameters are estimated using the least-squares method to solve the challenge of uncertainty in parameters. The Back-Stepping model, combined with the sliding mode, has benefited from the advantage of a sliding mode controller, namely, its robustness against uncertainties. The simulation results have demonstrated that the proposed controller has led tumor cells to zero with a higher velocity compared to the integer-order model controller and the adaptive fuzzy conventional Back-Stepping controller.

癌症是人类死亡的主要因素之一。本文的主要目的是提出和控制肿瘤治疗的免疫力。它可以自适应地受益于后退控制，滑模控制，模糊控制和参数估计的优势。提出的癌性肿瘤模型是多输入多输出（MIMO）非线性分数阶模型。本文设计了一种新的基于滑模控制器的反推模型，以解决收敛速度问题，实现了鲁棒控制器。设计了一种新的结合滑模方式的Back-stepping控制器，以解决收敛速度的挑战，并面对控制器的普通back-stepping鲁棒性问题。由于在不确定模型中考虑了非线性表达式，模糊控制器已被应用到模型中。使用最小二乘法估计参数，以解决参数不确定性的挑战。Back-Stepping模型与滑模相结合，得益于滑模控制器的优势，即其对不确定性的鲁棒性。仿真结果表明，与整数阶模型控制器和自适应模糊常规Back-Stepping控制器相比，该控制器以较高的速度将肿瘤细胞归零。