Singular perturbations in ergodic control of diffusions

Vivek S. Borkar; Vladimir Gaitsgory

doi:10.1137/060657327

Singular perturbations in ergodic control of diffusions

Vivek S. Borkar, Vladimir Gaitsgory

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

Abstract

Ergodic control of a nondegenerate diffusion with two time-scales is studied in the limiting case as the time-scale separation increases to infinity. It is shown that the limit problem is another ergodic control problem for the slow time-scale component alone, with its dynamics averaged over the (controlled) invariant probability measures for the fast component. These measures in turn can be treated as the "effective control variable."

Original language	English
Pages (from-to)	1562-1577
Number of pages	16
Journal	SIAM Journal on Control and Optimization
Volume	46
Issue number	5
DOIs	https://doi.org/10.1137/060657327
Publication status	Published - 2007
Externally published	Yes

Keywords

Controlled diffusions
Ergodic control
Invariant probability measures
Singular perturbations
Two time-scales

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10.1137/060657327

Cite this

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AB - Ergodic control of a nondegenerate diffusion with two time-scales is studied in the limiting case as the time-scale separation increases to infinity. It is shown that the limit problem is another ergodic control problem for the slow time-scale component alone, with its dynamics averaged over the (controlled) invariant probability measures for the fast component. These measures in turn can be treated as the "effective control variable."

KW - Controlled diffusions

KW - Ergodic control

KW - Invariant probability measures

KW - Singular perturbations

KW - Two time-scales

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Singular perturbations in ergodic control of diffusions

Abstract

Keywords

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