Distributed Learning for Echo State Networks with Dynamic Event-Triggered Consensus

This paper is devoted to studying the dynamic event-triggered consensus problem in distributed Echo State Networks (ESNs). The traditional ESN problem can be formulated as a set of distributed sub-problems with consensus constraints, which are solved using the Zero-Gradient-Sum (ZGS) distributed optimization strategy. Additionally, each agent employs a distributed dynamic event-triggered strategy based on its internal dynamic variables to achieve asymptotic consensus convergence. The purposeful dynamic triggering strategy is more communication-efficient compared to static triggering strategies and eliminates the need for continuous communication to update controllers or monitor triggering thresholds. Numerical simulation results are presented to validate the efficacy of the proposed algorithm.