Asymptotic method for solving the problem of transition process optimization in a three-tempo singularly perturbed system

Abstract

The problem of constructing a transition process with minimal energy costs for a linear singularly perturbed system containing three groups of variables with significantly different rates of change is considered. Asymptotic approximations to solving this problem are constructed in the form of an open-loop and feedback controls. The main advantage of the proposed computational procedures is that the original problem is split into three unperturbed optimal control problems of lower dimension.