| Summary: | Every element is a part of a structure. A structure requires connections and to study them necessitates representation. Network science bridges this gap, and studying their dynamics allows the system of nodes and edges to be observed and controlled. Simple individual agents in a network can exhibit complex behavior owing to their interaction. This found application in many multi agent systems including unmanned aerial vehicles that work together to achieve a common purpose. This study analyzed their consensus dynamics that allowed to capture the evolution of the agent's agreement on a common variable. To study the collective response behavior of the multi agent system, a driving node that acts as a leader is used to stimulate agents that are connected to them. The control of the networked system is decentralized by selecting the leader to be part of the network. The results are generalized by analyzing different network types such as ring network, random spatial network and, certain topologies such as topological and metric neighborhood. In studying the influence of single leader, in a simple ring network, it is clear that connectivity k has no effect on the system's ability to reach consensus. In random spatial network, consensus on the single leader's state is shown to be hard to reach due to directed communication. For a network that has multiple leaders, the set up was modified to keep the agents at a mid-point and allowed to evolve in two mutually exclusive directions, commanded by multiple leaders. The effect of this conflict is then quantified by the temporal oscillations in some of the agent's state and the appearance of deadlocks in the system's state.
An in-depth understanding on the collective dynamics response of this leader-follower networked system is derived by changing the network parameters. The findings show that when multiple leaders drive the system in conflicting direction, the system's response shows limitations in our freedom to setup network parameters such as the neighborhood connectivity k. This study is unique in the use of frequency domain analysis to understand collective behavior and observes the effect of connectivity ki on the network response. This study also explores the intertwining dynamics of consensus and conflict in Multi-Agent systems.
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