Distributed Controller Design and Analysis of Second-Order Signed Networks With Communication Delays

Area of Science:

• Control Theory
• Network Science
• Systems Engineering

Background:

• Distributed control systems are crucial for coordinating multiple agents.
• Signed networks incorporate both positive (cooperative) and negative (antagonistic) interactions.
• Achieving consensus in complex networks with delays presents significant challenges.

Purpose of the Study:

• To develop distributed control protocols for second-order signed networks.
• To establish necessary and sufficient conditions for consensus in these networks.
• To analyze the impact of communication delays on network consensus.

Main Methods:

• Design of distributed control protocols based on nearest neighbor rules.
• Mathematical analysis of consensus conditions for strongly connected signed digraphs.
• Development of a protocol to handle communication delays and determine delay margins.

Main Results:

• Necessary and sufficient conditions for consensus in second-order signed networks without delays were derived.
• A novel protocol was designed for networks with communication delays.
• Consensus can be achieved under a determined delay margin, even with communication delays.

Conclusions:

• The proposed distributed control protocols ensure consensus in second-order signed networks.
• The findings provide a theoretical framework for designing robust control systems in signed networks.
• The study validates the effectiveness of the consensus results through simulations.