Numerical constructions of optimal feedback in models of chemotherapy of a malignant tumor.

In this paper, a problem of chemotherapy of a malignant tumor is considered. Dynamics is piecewise monotone and a therapy function has two maxima. The aim of therapy is to minimize the number of tumor cells at the given final instance. The main result of this work is the construction of optimal feedbacks in the chemotherapy task. The construction of optimal feedback is based on the value function in the corresponding problem of optimal control (therapy). The value function is represented as a minimax generalized solution of the Hamilton-Jacobi-Bellman equation. It is proved that optimal feedback is a discontinuous function and the line of discontinuity satisfies the Rankin-Hugoniot conditions. Other results of the work are illustrative numerical examples of the construction of optimal feedbacks and Rankin-Hugoniot lines.