Transfer Operator Based Approach for Optimal Stabilization of Stochastic System
This work provides a novel method for optimal stabilization of stochastic nonlinear systems, which is important for control theory applications.
The paper develops a linear transfer Perron-Frobenius operator-based approach for optimal stabilization of stochastic nonlinear systems, extending a deterministic framework to stochastic cases with minimal changes. Simulation results verify the framework.
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.