Abstract
AbstractOptimal control problems for mathematical models describing HIV infection dynamics in a human body are considered in the paper. An overview of current approaches to solution of control problems for models of HIV dynamics is presented for techniques related to construction of optimal programme (open loop) or positional (feedback) controls for various criteria of control process quality and is based on the Pontryagin’s maximum principle and the Bellman’s theory of dynamic programming, respectively. In the framework of the theory of positional differential games of Krasovskii, there are constructive and efficient methods of synthesis of controls for different classes of dynamical systems. In this paper we present a formalization of a control problem for HIV infection considered as a corresponding positional differential game. The control algorithm based on the method of extremal shift is applied to the ODEs model of HIV infection. The numerical implementation of the extremal shift method is developed to construct the control taking the system to a neighbourhood of a given trajectory using the information on the dynamics of the guides or leaders.
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