[Paper Review] Synchronization for Multi-agent Systems under Directed Switching Topologies

Tao Yang, Ziyang Meng+3 more|arXiv (Cornell University)|Jan 25, 2014

Neural Networks Stability and Synchronization4 citations

TL;DR

This paper studies synchronization in multi-agent systems with time-varying, directed switching topologies, analyzing both leader-follower and leaderless networks. It establishes sufficient conditions for global exponential or asymptotic synchronization, showing that norm synchronization under fixed graphs implies state synchronization, and highlights key differences between directed and undirected communication structures.

ABSTRACT

We consider the synchronization problem for a network of state diffusive coupled agents with identical but time-varying dynamics under switching communication topologies. Both leader-follower and leaderless networks are studied. For leader-follower networks, sufficient conditions are established regarding the connectivity of communication graphs for the network to achieve global exponential or asymptotic synchronization, for directed and undirected communications respectively. For leaderless networks, sufficient conditions for global asymptotic norm synchronization are established, for directed and undirected communications respectively, in the sense that the norm of agent state converges to a common value. We also show that if the communication graph is fixed, norm synchronization leads to state synchronization. The results reveal some important similarities and differences between leaderless and leader-follower networks for synchronization under directed switching communication graphs. Examples illustrate the relations to the literature.

Motivation & Objective

• To investigate synchronization in multi-agent systems with time-varying, directed switching communication topologies.
• To establish sufficient conditions for global exponential and asymptotic synchronization in leader-follower networks under directed and undirected communication graphs.
• To derive conditions for global asymptotic norm synchronization in leaderless networks with directed and undirected topologies.
• To examine the relationship between norm synchronization and state synchronization when the communication graph is fixed.
• To clarify structural differences and similarities between leaderless and leader-follower networks under directed switching graphs.

Proposed method

• Utilizes state diffusive coupling to model agent interactions, ensuring dynamics are identical across agents.
• Applies graph-theoretic analysis to characterize connectivity of switching communication topologies, both directed and undirected.
• Employs Lyapunov-based stability analysis to derive sufficient conditions for exponential and asymptotic synchronization.
• Introduces norm synchronization as a key concept in leaderless networks, where the norm of agent states converges to a common value.
• Establishes that fixed topology leads to norm synchronization implying state synchronization, linking two synchronization types.
• Uses examples to illustrate theoretical findings and relate them to existing literature on switching topologies.

Experimental results

Research questions

• RQ1 What conditions ensure global exponential or asymptotic synchronization in leader-follower multi-agent systems with directed switching topologies?
• RQ2 How do directed and undirected communication graphs affect synchronization in leaderless multi-agent networks?
• RQ3 Under what conditions does norm synchronization imply state synchronization in fixed-topology networks?
• RQ4 What structural differences exist between leaderless and leader-follower networks in achieving synchronization under directed switching graphs?
• RQ5 How do the proposed conditions relate to existing results in the literature on switching topologies?

Key findings

• Sufficient conditions for global exponential synchronization are established for leader-follower networks under directed and undirected switching topologies.
• Global asymptotic norm synchronization is achieved in leaderless networks under both directed and undirected communication graphs.
• When the communication graph is fixed, norm synchronization implies state synchronization, linking two synchronization types.
• The results reveal distinct behaviors between leaderless and leader-follower networks under directed switching topologies, particularly in convergence properties.
• Examples demonstrate consistency with prior work and clarify the role of graph connectivity and directionality in synchronization dynamics.