Program and Positional Control Strategies for the Lotka–Volterra Competition Model

Abstract

In this notice, we consider a control model of cancer dynamics that describes the interaction between normal and cancer cells and is based on the Lotka–Volterra competition model. For this control model, we consider a minimization problem of a terminal functional, which is a weighted difference of the concentrations of cancer and normal cells at the final moment of treatment. For this model, we consider three types of treatment. For each type, using the Pontryagin maximum principle, we analyze and establish properties of the optimal controls and illustrate the analytical findings by numerical calculations. Moreover, apart from the optimal controls, we also construct the positional controls for two variants of control constraints.