Stability in dynamic event-triggered control of stochastic nonlinear systems: A G-Brownian motion scenario

In this paper, the event-triggered stabilization problem for stochastic nonlinear systems driven by G-Brownian motion (G-SNSs) is investigated. To this end, as a promotion of noise-dependent control, a novel exponential G-noise-related dynamic event-triggered controller is designed to stabilize the systems. Compared to existing research on event-triggered control (E-TC) in traditional stochastic systems, the constraint of normal distribution is removed, which facilitates the description of uncertainties in probabilities and models. Note that when focusing on G-SNSs, current theories on event-triggered stabilization are ineffective, since the G-SNS is established within a sub-linear expectation framework. To address this challenge, we construct a continuous-time control system driven by G-Brownian motion as an auxiliary system and employ the model transformation method to analyze stability. More specifically, by exploring the favorable effect of G-noise, a novel stability criterion is proposed that offers broader applicability than the existing Lyapunov condition under G-expectation, where the Lyapunov function employed in this study is not required to have a strictly negative definite infinitesimal generator. Subsequently, through a detailed comparison between the auxiliary system and the E-TC system, the moment exponential stability of the E-TC system at arbitrary order (p⩾0) is established, which potentially encompasses the results of quasi-sure exponential stability. Finally, the theoretical results are applied to a second-order spring-damping system, with corresponding numerical simulations being provided.