Consensus Dynamics in Multi-Agent Systems Considering Efficiency and Fairness

Consensus Dynamics in Multi-Agent Systems studies how individual agents interact to reach a common agreement on a specific state. Consensus algorithms are essential in many applications, including network engineering systems and cooperative robotics. Efficiency is measured by how fast the agents reach consensus. Faster convergence can be obtained in fewer computational iterations using less communication. In this project, the connectivity and stability of the system were checked since the system must be designed to ensure that all agents converge to a single value in a given time. We computed and plotted the Gershgorin circles for the Laplacian matrix of the multi-agent system considered. The adjacency matrix defines the communication links between the agents, with each edge weighting 1. The eigenvalues of the Laplacian matrix are computed and plotted to analyze the efficiency in the consensus dynamics.

There is a trade-off between efficiency and fairness. Algorithms prioritizing fast convergence may allow specific agents to dominate decision-making, reducing fairness. On the other hand, highly fair algorithms may sacrifice convergence speed to ensure equal influence across all agents. We aimed to design consensus algorithms that balance this trade-off, achieving both efficiency and fairness.