Stochastic Stabilization for Nonlinear Systems: A Noise-Compensated Prediction Scheme

This article investigates the predictor-based stabilization by noise for nonlinear systems. A novel concept, the noise-compensated auxiliary ordinary differential equation (ODE), is introduced to simulate system behavior, predict system state, and compensate for delay effects in the corresponding stochastic differential equation (SDE). Utilizing the auxiliary ODE, a predictor-based stabilizing noise is designed. Unlike conventional predictor-based schemes for stochastic systems, the proposed approach fully accounts for stochastic influences while generating state values that can be directly utilized for control. The proposed scheme is further applied to networked control systems (NCSs) under dual-channel packet loss, where the number of consecutive packet losses is allowed to be unbounded. In this way, the conventional assumption of a finite upper bound on packet loss is removed, and the system stability is guaranteed even under arbitrarily high-packet loss rates. To showcase the superiority of the proposed methodology, numerical simulations are conducted.