Transfer operator-based approach for optimal stabilization of stochastic systems

In this paper, we develop linear transfer Perron-Frobenius operator-based approach for optimal stabilization of stochastic nonlinear systems. One of the main highlights of the proposed transfer operator based approach is that both the theory and computational framework developed for the optimal stabilization of deterministic dynamical systems 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.