This paper studies practical event-triggered intermittent stabilization for stochastic differential equations driven by $G$-Brownian motion. A nonlinear feedback controller is applied only on prescribed active windows and is implemented through the latest transmitted state. The triggering rule contains a constant practical threshold, which leads to an ultimate bound in the mean-square estimate and provides a positive margin for excluding Zeno behavior. Under explicit Lyapunov conditions, practical exponential stability in $G$-mean square is established with an explicit decay rate and residual bound. When the constant threshold is removed, the residual term disappears and, provided that the closed-loop solution is globally defined quasi-surely, a capacity Borel–Cantelli argument yields quasi-sure exponential stability. For a positive constant threshold, quasi-sure Zeno-freeness is proved by a finite-horizon increment estimate and a capacity argument. A nonlinear example illustrates the theoretical conditions.
Citation: Bingjun Wang, Mingxia Yuan. Practical event-triggered intermittent stabilization of stochastic differential equations driven by $ G $-Brownian motion via nonlinear feedback[J]. Electronic Research Archive, 2026, 34(12): 9438-9461. doi: 10.3934/era.2026396
This paper studies practical event-triggered intermittent stabilization for stochastic differential equations driven by $G$-Brownian motion. A nonlinear feedback controller is applied only on prescribed active windows and is implemented through the latest transmitted state. The triggering rule contains a constant practical threshold, which leads to an ultimate bound in the mean-square estimate and provides a positive margin for excluding Zeno behavior. Under explicit Lyapunov conditions, practical exponential stability in $G$-mean square is established with an explicit decay rate and residual bound. When the constant threshold is removed, the residual term disappears and, provided that the closed-loop solution is globally defined quasi-surely, a capacity Borel–Cantelli argument yields quasi-sure exponential stability. For a positive constant threshold, quasi-sure Zeno-freeness is proved by a finite-horizon increment estimate and a capacity argument. A nonlinear example illustrates the theoretical conditions.
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Figures(2)
Bingjun Wang, Mingxia Yuan. Practical event-triggered intermittent stabilization of stochastic differential equations driven by $ G $-Brownian motion via nonlinear feedback[J]. Electronic Research Archive, 2026, 34(12): 9438-9461. doi: 10.3934/era.2026396
Hybrid event-triggered intermittent control mechanism. (a) Alternating active and rest windows: the active window $ [t_k, s_k) $ is followed by the rest window $ [s_k, t_{k+1}) $. (b) Zoom into an active window: at each triggering instant the condition is evaluated; if it is satisfied, the control input is updated; otherwise the previous value is held. The active window is terminated at $ s_k $
Numerical simulation results for the event-triggered intermittent control scheme: (a) mean-square trajectory; the red dashed line indicates the empirical ultimate bound; (b) inter-event intervals
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