A Dual Approach for Positive T-S Fuzzy Controller Design and Its Application to Cancer Treatment Under Immunotherapy and Chemotherapy

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-Sugen. 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 copositive 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, which can be solved very efficiently. Finally, the simulation results show the effectiveness of the proposed control approach for the cancer treatment. Keywords: Co-positive linear Lyapunov function, Cancer, Chemotherapy, Immunotherapy, Positive system, Takagi-Sugeno fuzzy system.