# Transfer Operator Based Approach for Optimal Stabilization of Stochastic System

## TL;DR

This paper introduces a transfer operator-based method for the optimal stabilization of stochastic nonlinear systems, extending deterministic approaches with minimal modifications and demonstrating effectiveness through simulations.

## Contribution

It develops a transfer Perron Frobenius operator approach for stochastic systems, bridging deterministic and stochastic stabilization techniques with a new computational framework.

## Key findings

- Framework successfully stabilizes stochastic nonlinear systems
- Finite-dimensional approximations enable practical computations
- Simulation results confirm the effectiveness of the approach

## 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.