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JOURNALS // Teoriya Veroyatnostei i ee Primeneniya // Archive

Teor. Veroyatnost. i Primenen., 1997 Volume 42, Issue 3, Pages 627–632 (Mi tvp2006)

This article is cited in 9 papers

Short Communications

Optimality almost surely and in probability for a stochastic linearly quadratic regulator

E. L. Presman

Central Economics and Mathematics Institute, RAS

Abstract: The stochastic linear quadratic regulator with constant coefficients is considered in continuous time when the horizon tends to infinity. It is shown that the feedback control, which is optimal for the infinite time horizon in the corresponding deterministic problem is optimal in probability for any rate function which tends to zero and almost sure for any power rate function with negative degree.

Keywords: linear quadratic regulator, optimality almost surely, optimality in probability, stabilizability, detectability.

Received: 06.08.1996

DOI: 10.4213/tvp2006


 English version:
Theory of Probability and its Applications, 1998, 42:3, 531–535

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