TY - JOUR

T1 - Tail-constraining stochastic linear-quadratic control

T2 - A large deviation and statistical physics approach

AU - Chertkov, Michael

AU - Kolokolov, Igor

AU - Lebedev, Vladimir

PY - 2012/8

Y1 - 2012/8

N2 - 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.

AB - 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.

KW - large deviations in non-equilibrium systems

KW - robust and stochastic optimization

UR - http://www.scopus.com/inward/record.url?scp=84866321626&partnerID=8YFLogxK

U2 - 10.1088/1742-5468/2012/08/P08007

DO - 10.1088/1742-5468/2012/08/P08007

M3 - Article

AN - SCOPUS:84866321626

VL - 2012

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

SN - 1742-5468

IS - 8

M1 - P08007

ER -