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Standard definition of the stochastic Risk-Sensitive Linear-Quadratic (RS-LQ)control depends on the risk parameter, which is normally left to be setexogenously. We reconsider the classical approach and suggest two alternativesresolving the spurious freedom naturally. One approach consists in seeking forthe minimum of the tail of the Probability Distribution Function (PDF) of thecost functional at some large fixed value. Another option suggests to minimizethe expectation value of the cost functional under constraint on the value ofthe PDF tail. Under assumption of the resulting control stability, bothproblems are reduced to static optimizations over stationary control matrix.The solutions are illustrated on the examples of scalar and 1d chain (string)systems. Large Deviation self-similar asymptotic of the cost functional PDF isanalyzed.

Tail-Constraining Stochastic Linear-Quadratic Control: Large Deviation and Statistical Physics Approach