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Consensus over directed static networks with arbitrary finite communication delays.
Jianquan Lu1, Daniel W C Ho, Jürgen Kurths
1Department of Mathematics, Southeast University, Nanjing, People's Republic of China. jqluma@gmail.com
Summary
Consensus is achievable in directed networks with communication delays, even unknown ones. A single informed leader can regulate all node states, regardless of coupling type or signal strength.
Area of Science:
- Control Theory
- Network Science
- Systems Engineering
Background:
- Consensus problems are crucial in distributed systems, aiming for agreement among agents.
- Directed networks with communication delays present significant challenges to achieving consensus.
- Limited local information availability complicates distributed coordination.
Purpose of the Study:
- To investigate consensus in directed static networks with arbitrary communication delays.
- To analyze the impact of linear and nonlinear coupling on network consensus.
- To determine the conditions under which consensus can be robustly achieved.
Main Methods:
- Analysis of networked systems with locally available, delayed information.
- Mathematical formulation of consensus conditions in directed graphs.
- Theoretical proof of consensus achievability irrespective of delay values.
- Demonstration of leader-based state regulation.
Main Results:
- Consensus is guaranteed regardless of communication delay magnitudes.
- Explicit knowledge of communication delays is not required for consensus.
- A single, well-informed leader node can effectively regulate all other nodes' states.
- The leader's influence is effective even with weak external signals.
Conclusions:
- The proposed framework enables robust consensus in complex directed networks.
- Leader-based control offers a powerful strategy for achieving distributed agreement.
- The findings have implications for opinion dynamics and distributed decision-making.
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