Extended Linearization Method in the Problem of Drug Administration in Cancer Treatment

This paper presents an "extended linearization"method for control synthesis for a nonlinear system of differential equations. The method is based on converting the original nonlinear model into an equal linear-like form with state-dependent parameters. This approach allowed the system to be transformed in such a way as to transition to the Riccati equation, but with state-dependent parameters. This was necessary in order to avoid the Hamilton-Jacobi-Bellman equation. A search for the solution of the equation at each time point was performed. The results of the synthesis of control actions were demonstrated on a model of drug therapy in the treatment of cancer, which considers the interaction of cancer, normal and immune cells. Several cases with different initial conditions and regulator parameters were considered for comparative analysis.