Adaptive back-stepping cancer control using Legendre polynomials

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.