| Summary: | In this paper we control the amount of three major biological cell types (normal, immune and tumor cells) under uncertainty in cancer model parameters, using different chemotherapy drug dosages. To achieve this goal, an adaptive robust controller is proposed for a third order nonlinear model, which consists of the interaction between normal, immune and tumor cells. We adjust the drug dosages to control the tumor growth and maintain immune and normal cells in their desired values. Due to tumor micro-environmental and biological changes and measurement inaccuracies, the exact quantity of the model parameters is not available. Therefore, it is necessary to design the controller in a way that it is robust against parameters uncertainty and variations, the proposed robust adaptive controller manipulates the drug dosages and estimates the parameters of the model, simultaneously. The resulting system is robust against parameters uncertainty and variations. The global stability and tracking convergence of the controller is proved using time-varying Lyapunov function. Moreover, extended Kalman filter observer is applied to estimate the immune cells, due to the difficulty measuring them during the biological in vivo experiments. The performance of the proposed controller and observer are investigated by computational results. Computational results show the desired effect of drug dosage injections on the normal, immune and tumor cells. We observe that the controller guarantees the robust performance against the parameters uncertainty. The extended Kalman filter observer has effective performance and estimates the immune cells with high accuracy. This approach could impact robust tumor control using appropriate drug dosages while the parameters of the model change over time in a patient and across different patients. Keywords: Cancer, Chemotherapy, Robust control, Kalman filter.
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