A dual approach for positive T–S fuzzy controller design and its application to cancer treatment under immunotherapy and chemotherapy. (April 2020) - Ahmadi, Elham; Zarei, Jafar; Razavi-Far, Roozbeh; Saif, Mehrdad
Highlights: Based on the dual approach for the positive systems, a positive T-S fuzzy controller for a successful treatment of the cancer under mixed immunotherapy and chemotherapy is proposed. By using the proposed control strategy, the number of fuzzy rules that inherently affects the conservatism, is dramatically reduced. The proposed framework incorporates a new T-S fuzzy model, linear co-positive Lyapunov function, and parallel distributed compensation with convex optimization approaches. Exploiting the control structure for the tumor-immune system in order to minimize the volume of the tumor cells and reducing the doses of the consumed drug. The proposed control structure prevents the tumor growth and lead to reach the density of immune competent cells at an acceptable level. Abstract: This study proposes an effective positive control design strategy for cancer treatment by resorting to the combination of immunotherapy and chemotherapy. The treatment objective is to transfer the initial number of tumor cells and immune–competent cells from the malignant region into the region of benign growth where the immune system can inhibit tumor growth. In order to achieve this goal, a new modeling strategy is used that is based on Takagi–Sugeno. A Takagi-Sugeno fuzzy model is derived based on the Stepanova nonlinear model that enables a systematic design of the controller. Then, a positive Parallel Distributed Compensation controller is proposed based on a linear co-positive Lyapunov Function so that the tumor volume and administration of the chemotherapeutic and immunotherapeutic drugs is reduced, while the density of the immune-competent cells is reached to an acceptable level. Thanks to the proposed strategy, the entire control design is formulated as a Linear Programming problem. Finally, the simulation results show the effectiveness of the proposed control approach for the cancer treatment.