Asymptotic behavior of the Bellman function in a stochastic optimal control problem (original) (raw)

Journal of Applied Mathematics and Mechanics, 1981

Abstract

ABSTRACT A quasi-optimal control giving a near-optimal result under small power resources is found by studying the asymptotic behavior of the Bellman function of the optimal control problem for the motion of a system perturbed by white noise with limited control power resources. The determination of the asymptotic behavior of the Bellman function and of the quasi-optimal control calls for solving the partial differential equations introduced in /1/. A converging iteration process is found for solving them.

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