Event-triggered scaled consensus for distributed networks in a compound noisy environment over markovian switched topologies

This article focuses on event-triggered scaled consensus for stochastic multi-agent systems (SMASs) in the presence of multiplicative and additive noises in a Markovian switched setting. First, a novel distributed stochastic approximation controller and event-triggered strategy are proposed for achieving the scaled consensus. Some sufficient criteria for realizing the event-triggered scaled consensus for SMASs under a compound noisy setting, are obtained by employing a new semi-decomposition procedure. In addition, scaled consensus implies that some agents converge on some different value by a certain proportion, thus the error transform method will fail if the network involved with multiplicative noise, which further implies that existing Lyapunov based technique in handling consensus results of additive noises will failure to function. In order to handle it, the boundedness of agents’ state is first given, and then the scaled consensus may be accomplished. Ultimately, our theoretical results are verified in mean square sense by two numerical simulations.