Title :
On Endogenous Random Consensus and Averaging Dynamics
Author :
Touri, Behrouz ; Langbort, Cedric
Author_Institution :
Dept. of Electr., Comput., & Energy Eng., Univ. of Colorado Boulder, Boulder, CO, USA
Abstract :
Motivated by various random variations of the Hegselmann-Krause model for opinion dynamics and gossip algorithm in an endogenously changing environment, we propose a general framework for the study of endogenously varying random averaging dynamics, that is, averaging dynamics whose evolution suffers from history-dependent sources of randomness. We show that under general assumptions, such dynamics is convergent almost surely. We also determine the limiting behavior and show that infinitely many time-varying Lyapunov functions are admitted.
Keywords :
Lyapunov methods; matrix algebra; random processes; time-varying systems; Hegselmann-Krause model; averaging dynamics; endogenous random consensus; time-varying Lyapunov functions; Aerodynamics; Control systems; Convergence; Heuristic algorithms; Random processes; Stochastic processes; Vectors; Stochastic systems; complex networks; distributed computing; distributed control;
Journal_Title :
Control of Network Systems, IEEE Transactions on
DOI :
10.1109/TCNS.2014.2337973