Neural controller for targeting a desired stationary distribution in stochastic systems

Abstract

One of the major missions in the field of stochastic control is to design efficient control policies that guarantee the stochastic systems stabilize within some specified stationary distribution. In this paper, we propose a neural controller based on the stochastic asymptotic stability theory and the condition of detailed balance. A novel physics-informed learning procedure is introduced to update the parameters in a multi-output neural network which is utilized to approximate the controller. We also prove rigorously that the proposed controller is unique if it exists, which is essential in applications. Furthermore, several representative stochastic systems are used to illustrate the usefulness of this neural controller for the stabilization of these dynamical systems in distribution.