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This paper deals with the control of a cancerous tumour growth. The model used is a Three-Dimensional Cancer Model (TDCM). The competition terms include tumour cells, healthy cells, and immune cells. Nature of the competition among the populations of tumour cells, healthy host cells, and immune cells results in a chaotic behaviour. In this paper, a nonlinear active control has been used to control the growth of a tumour. Effect of chemotherapy drug on the different cell populations has been studied. Our control objective is to control the tumour growth and minimize its population to a small value which can be considered as harmless.Along with the above objective, the normal cell population is also be maintained at a particular level. This work has been done completely inin-sillico environment. The simulation results are shown extensively to support the theoretical analysis and confirmed that the preliminary objectives of the paper are attained.

Chemotherapy as a cancer treatment has garnered much scientific interest in recent years. Chemotherapy is essential for the elimination of cancer cells to the greatest extent possible. Clinical studies demonstrate a predictable trajectory of tumor volume after chemotherapy. However, the standard dose regimens often utilized in chemotherapy have substantial toxicity and little therapeutic value. Consequently, optimum drug dosage is crucial for effectively reducing the tumor size to a defined level while tracking a predefined course. This work establishes optimum control theory with L1-norm based cost function to discover the inputs that decrease the difference between real tumor growth and goal size to improve treatment efficacy while minimizing the side effects. Because of the bang-off nature of the L1-norm control profile, intermittent drug dosing is possible. This study also compares and contrasts the findings with the cost function based on L2-norm. Simulation findings validate the performance of the proposed control scheme for chemotherapy. Further study is needed to confirm the procedures in clinical situations and optimize the regimens for individual patients.

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