Mathematical Investigation of Optimal Control of a Tumor Growth Model Drug Administration

This study investigates the optimal control problem for tumor growth dynamics, focusing on the existence and uniqueness of solutions. We derive necessary optimality conditions and prove the optimal control exists and is unique using the fixed‐point theorem. As our objective function includes weighted ‐ and ‐norms of controls, we first establish the existence and uniqueness of optimal control for ‐type problem and derive its optimal control form. Furthermore, due to the aggressive nature of the cytotoxic drug and the importance of determining its optimal dose during treatment, we considered the objective function to be linear with respect to this drug and referred to it as an ‐type problem. Next, we illustrate the relationship between the solutions of ‐type and ‐type problems. Additionally, using the Pontryagin Minimum Principle for ‐type optimal control problem, we demonstrate numerically that the resulting optimal control is nonsingular. The relationship between the optimal control obtained from solving the problem directly and the results from its analytical solution is numerically demonstrated.