On the asymptotics of the optimal value of the performance functional in a linear optimal control problem

摘要

We consider the asymptotics of the optimal value of the performance functional in an optimal control problem for a linear system with rapid and slow variables, with convex terminal performance functional depending on the slow variables, and with smooth geometric constraints on the control. We find sufficient conditions for the regularity of asymptotics and construct an algorithm for finding the complete asymptotics of the optimal value of the performance functional.