Title: Transfer Operator Based Approach for Optimal Stabilization of Stochastic System,
Abstract: In this paper we develop linear transfer Perron Frobenius operator-based
approach for optimal stabilization of stochastic nonlinear system. One of the
main highlight of the proposed transfer operator based approach is that both
the theory and computational framework developed for the optimal stabilization
of deterministic dynamical system in [1] carries over to the stochastic case
with little change. The optimal stabilization problem is formulated as an
infinite dimensional linear program. Set oriented numerical methods are
proposed for the finite dimensional approximation of the transfer operator and
the controller. Simulation results are presented to verify the developed
framework.