Inverse extremal problem for an anti-tumor therapy model

TL;DR

This paper addresses an inverse extremal control problem for a tumor growth model, aiming to minimize tumor cell density within tissue constraints, and develops an algorithm with demonstrated numerical efficiency.

Contribution

It introduces a novel inverse extremal control framework for tumor therapy modeling and provides a practical algorithm for solving the associated optimal control problem.

Findings

Proved solvability of the control problem.

Developed an effective algorithm for the control problem.

Demonstrated algorithm efficiency through numerical example.

Abstract

An optimal control problem for a model of tumor growth is studied. In a given subdomain, it is required to minimize the density of tumor cells, while the drug concentration in tissue is limited by given minimal and maximal values. Based on derived estimates of the solution of the controlled system, the solvability of the control problem is proved. The problem is reduced to an optimal control problem with a penalty. An algorithm for solving the optimal control problem with a penalty is constructed and implemented. The efficiency of the algorithm is illustrated by a numerical example.