A Reset Algorithm Solving Coordination With Antagonistic Reciprocity
Yan Zhang, Yang Liu, Xinsong Yang, Jianlong Qiu · IEEE Transactions on Systems Man and Cybernetics Systems · 2021
This article is dedicated to solving the coordination problem using a reset algorithm that consists of linear impulsive dynamics, over which antagonistic reciprocity among interacting individuals is inevitable. It shows that reciprocal agents are convergent (including consensus and clusters) whenever the scaling parameters of an agent, corresponded to continuous/discrete dynamics, enjoy the same proportion value that matches to all agents. Otherwise, all participating agents share nothing eventually, that is, they achieve stability. This immediately gives rise to that the final aggregated values of agents are entirely determined by the underlying parameters, on condition that the connection property of communication topologies is preserved. Therefore, the proposed setup features a unified perspective on consensus, clusters (including bipartite consensus), and stability that are separately studied in most of the existing literature. The developed method is well supported via numerical examples.