Asymptotics of solving control problem with minimum intensity of linear three-tempo singularly perturbed system

The problem of optimizing the transient process in a linear singularly perturbed system with two groups of fast variables is considered, which consists in finding multidimensional control with minimal intensity. It is shown that to construct an approximate (in the asymptotic sense) solution to this problem, it is sufficient to solve three unperturbed optimal control problems of a smaller dimension.