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

Michael Chertkov, Igor Kolokolov, Vladimir Lebedev

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article numberP08007
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number8
Publication statusPublished - Aug 2012
Externally publishedYes


  • large deviations in non-equilibrium systems
  • robust and stochastic optimization


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