Optimal Control Problem for a Differential Inclusion with Rapidly Oscillating Coefficients on the Semiaxis.

We study the optimal control problem for a system of differential inclusions with rapidly oscillating coefficients on the semiaxis. For this purpose, we use the averaging method. The solvability of the original exact problem and the corresponding averaged problem is substantiated. It is proved that the optimal controls and optimal trajectories of solutions of the exact problem converge to the optimal control and optimal trajectory of solutions of the averaged problem. It is also shown that the optimal control of the averaged problem is "almost" optimal for the original exact problem. [ABSTRACT FROM AUTHOR]