On the application of the averaging method to one problem of optimal control with unfixed time
Abstract
UDC 517.9
We consider the problem of optimal control for a system of differential equations with rapidly oscillating coefficients and a coercive target functional. The final time is not fixed. It is defined as the first time of hitting of a given closed bounded subset of the phase space by the phase point. The solvability of this problem is proved, and the convergence of the optimal solutions of the original problem to the optimal process of the problem with averaged parameters is justified.
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