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In this paper we develop linear transfer Perron Frobenius operator-basedapproach for optimal stabilization of stochastic nonlinear system. One of themain highlight of the proposed transfer operator based approach is that boththe theory and computational framework developed for the optimal stabilizationof deterministic dynamical system in [1] carries over to the stochastic casewith little change. The optimal stabilization problem is formulated as aninfinite dimensional linear program. Set oriented numerical methods areproposed for the finite dimensional approximation of the transfer operator andthe controller. Simulation results are presented to verify the developedframework.

Transfer Operator Based Approach for Optimal Stabilization of Stochastic System