Distributed Hybrid Dynamic Event-Triggered Consensus Control for Nonlinear Multi-Agent Systems

This article addresses both leaderless and leader-following consensus issues for Lipschitz nonlinear multi-agent systems. To begin with, the issues are discussed in view of leaderless scenarios. Firstly, a distributed dynamic event-triggered mechanism is introduced to mitigate continuous communication burdens among neighboring agents. This mechanism incorporates an open-loop estimation algorithm and an inner self-learning term into the triggering conditions. Secondly, to prevent Zeno behavior, a time/event hybrid mechanism is implemented. For each agent, based on the local state information at the current event-triggered instant and the recent event-triggered instant receiving from neighbors, open-loop state estimations are conducted. Then, by utilizing these open-loop state estimations, a distributed adaptive control protocol is developed within the framework of the hybrid dynamic event-triggered mechanism, including an updating mechanism for the coupling strength of each agent. The challenge posed by the Lipschitz nonlinearity is addressed by solving a Riccati equation. Additionally, the proposed method is improved to be suitable for leader-following multi-agent systems. Finally, simulation examples demonstrate the effectiveness of the proposed method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The purpose of this paper is to introduce a hybrid dynamic event-triggered mechanism aimed at reducing the communication load in Lipschitz nonlinear multi-agent systems. By integrating a hybrid mechanism that combines both time-based and event-based triggers, the proposed scheme effectively minimizes unnecessary data exchanges among agents while naturally excluding the Zeno behavior. This is particularly advantageous in practical scenarios where bandwidth is limited or efficiency in data transmission is highly required in applications. The introduction of open-loop estimators ensures that continuous communication between two neighboring agents is not required. Furthermore, the introduction of an adaptive control protocol, which incorporates a projection algorithm for dynamically adjusting coupling gains, ensures that the interactions between agents remain within safe operational limits. The projection algorithm ensures that the adaptive gain remains within a prescribed range, thus preventing it from growing excessively and preserving system stability.