Stochastic Stabilization Subject to Actuator Saturation via Drifting Stochastic Noise

This paper discusses the stabilization of linear stochastic systems subject to actuator saturation, where the stochastic noise is applied to the controller for stabilization purposes. The saturation function is modeled as a switching function. We propose that an Itô system with actuator saturation can be locally and stochastically stable, followed by the solution of the original domain of attraction (DoA). To extend the original DoA globally, a drifting value is added to the Brownian motion, achieving global and almost sure exponential stability. However, when considering stochastic noise in saturation, it is challenging to model the drifting Brownian motion in the saturation function. Thus, a drifting-probability random walk process is used to replace the drifting Brownian motion. A discrete sampling stochastic controller is designed, which can achieve local and almost sure exponential stability. Finally, a simulation is conducted to demonstrate the effectiveness of this proposed discrete sampling stochastic controller.