Fully Distributed Event-Triggered Protocols for Linear Multi-Agent Networks (1807.05326v1)

Abstract: This paper considers the distributed event-triggered consensus problem for general linear multi-agent networks. Both the leaderless and leader-follower consensus problems are considered. Based on the local sampled state or local output information, distributed adaptive event-triggered protocols are designed, which can ensure that consensus of the agents is achieved and the Zeno behavior is excluded by showing that the interval between any two triggering events is lower bounded by a strictly positive value. Compared to the previous related works, our main contribution is that the proposed adaptive event-based protocols are fully distributed and scalable, which do not rely on any global information of the network graph and are independent of the network's scale. In these event-based protocols, continuous communications are not required for either control laws updating or triggering functions monitoring.

• The paper introduces fully distributed consensus protocols that use local information to achieve both leaderless and leader-follower coordination.
• It employs adaptive event-triggered control with techniques like σ-modification to enhance robustness and mathematically guarantee positive intervals between events, thereby eliminating Zeno behavior.
• Numerical simulations validate the protocols' effectiveness and stability across different network topologies, reducing reliance on continuous communication in resource-constrained environments.

Overview of Fully Distributed Event-Triggered Protocols for Linear Multi-Agent Networks

The paper by Cheng and Li addresses a critical problem in the field of cooperative control within networked multi-agent systems: the development of fully distributed event-triggered consensus protocols for general linear multi-agent networks. Traditional consensus methods are often constrained by the need for continuous communication and global network information, limiting their scalability and applicability in networked control applications where bandwidth and energy resources are limited. This paper makes significant contributions by proposing scalable protocols that solely rely on local information, obviating the necessity for global eigenvalue knowledge of the communication graph, and eliminating the Zeno behavior concern.

Main Contributions

1. Leaderless and Leader-Follower Consensus: The authors address both the leaderless and leader-follower consensus problems. They propose an adaptive event-based protocol for leaderless consensus that incorporates sampled state information and time-varying weights in control laws and triggering functions. For scenarios where relative state information isn't accessible, they offer an observer-based adaptive protocol relying on local output information only.
2. Exclusion of Zeno Behavior: A pivotal aspect of the proposed protocols is their ability to rule out Zeno behavior. The authors demonstrate mathematically that the interval between two consecutive event-triggering instants maintains a strictly positive lower bound, ensuring practical implementability.
3. Adaptive Event-Based Protocol Design: The proposed protocols leverage adaptive control strategies to ensure robustness against external disturbances. The protocols incorporate innovations from the adaptive control literature, such as the σ-modification technique, enhancing their adaptability and stability.
4. Numerical Simulations: The efficacy of the proposed protocols is validated through numerical simulations that demonstrate consensus achievement and the stability of adaptive coupling weights. These simulations provide critical insight into the performance of the protocols across different communication topologies.

Practical and Theoretical Implications

The fully distributed nature of the proposed event-triggered protocols has significant practical implications. By eliminating the requirement for continuous communication and global network information, these protocols are particularly well-suited for implementation in resource-constrained environments such as sensor networks, robotic swarms, and distributed control systems in which wireless communication is prevalent.

Theoretically, this work advances the understanding of consensus protocols by addressing the limitations of previous approaches that necessitate global insight into the network structure. This shift from global to local reliance marks an evolution in the field's approach to distributed control problems.

Future Directions

Potential future advancements in this domain could involve extending the proposed techniques to incorporate dynamically changing network topologies or addressing more complex multi-agent systems with nonlinear dynamics. Moreover, exploring the interplay between event-triggered control and machine learning techniques might offer promising avenues for further research, particularly in the adaptation of control protocols based on online learning algorithms.

In summary, Cheng and Li's work presents a notable advancement in the development of scalable, robust, and fully distributed event-triggered protocols for multi-agent systems. By addressing key challenges in networked cooperative control, this paper lays the groundwork for future research efforts aimed at broadening the application scope and enhancing the efficacy of distributed control algorithms in complex, dynamic environments.