Abstract. This paper considers an optimal control problem, which is described by a system of differential equations with fast and slow variables and boundary conditions on fast variables. Conditions that guarantee construct of asymptotic approximation to a solution in the conditionally stable case, which is being used for an averaged optimal control problem for slow variables, are imposed upon a fast subsystem. The paper provides an algorithm, which allows to construct an optimal control of the given optimal control problem, by means of an optimal control of the averaged problem. Found solutions are also being assessed.

Received: January 24, 2013

AMS Subject Classification: 34B15, 34C29, 34K35

Key Words and Phrases: averaging method, boundary value problem, slow and fast variables, conditionally stable case, optimal control problem

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