Constructive method for solving a linear minimax problem of optimal control

In this paper, we propose a constructive method for solving a linear minimax problem of optimal control. Following the Gabasov-Kirillova approach, we introduce the concept of so-called support control. After establishing an optimality criterion for the support control, we describe a scheme for reducing the initial infinite-dimensional problem to a finite-dimensional one, which can be solved numerically by the methods of linear programming. At the end, we give an illustrative example.