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.