Michael Chertkov, Igor Kolokolov, Vladimir Lebedev
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 to minimize the expectation value of the cost functional under constraint on the value of the PDF tail. Under assumption of stability, both problems 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 is analyzed.
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http://arxiv.org/abs/1204.0820
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