Tail-constraining stochastic linear-quadratic control: a large deviation and statistical physics approach

The standard definition of the stochastic risk-sensitive linear-quadratic (RS-LQ) control depends on the risk parameter, which is normally left to be set exogenously. We reconsider the classical approach and suggest two alternatives, resolving the spurious freedom naturally. One approach consists in...

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Bibliographic Details
Published in:Journal of statistical mechanics 2012-08, Vol.2012 (8), p.P08007-16
Main Authors: Chertkov, Michael, Kolokolov, Igor, Lebedev, Vladimir
Format: Article
Language:English
Subjects:
Asymptotic properties
Cost engineering
Deviation
Optimization
Probability density functions
Scalars
Self-similarity
Stochasticity
Online Access:Get full text
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Summary:The standard definition of the stochastic risk-sensitive linear-quadratic (RS-LQ) control depends on the risk parameter, which is normally left to be set exogenously. We reconsider the classical approach and suggest two alternatives, resolving the spurious freedom naturally. One approach consists in seeking for the minimum of the tail of the probability distribution function (PDF) of the cost functional at some large fixed value. Another option suggests minimizing the expectation value of the cost functional under a constraint on the value of the PDF tail. Under the assumption of resulting control stability, both problems are reduced to static optimizations over a stationary control matrix. The solutions are illustrated using the examples of scalar and 1D chain (string) systems. The large deviation self-similar asymptotic of the cost functional PDF is analyzed.
ISSN:1742-5468
1742-5468
DOI:10.1088/1742-5468/2012/08/P08007