On convergence rate of a continuous-time distributed self-appraisal model with time-varying relative interaction matrices

Weiguo Xia, Ji Liu, Tamer Basar, Xi Ming Sun

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper studies a recently proposed continuous-time distributed self-appraisal model with time-varying interactions among a network of n individuals which are characterized by a sequence of time-varying relative interaction matrices. The model describes the evolution of the social-confidence levels of the individuals via a reflected appraisal mechanism in real time. We show that when the relative interaction matrices are doubly stochastic, the n individuals' self-confidence levels will all converge to 1/n, which indicates a democratic state, exponentially fast under appropriate assumptions, and provide an explicit expression for the convergence rate. Numerical examples are provided to verify the theoretical results and to show that when the relative interaction matrices are stochastic (not doubly stochastic), the social-confidence levels of the individuals may not converge to a steady state.

Original languageEnglish (US)
Title of host publication2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4076-4081
Number of pages6
ISBN (Electronic)9781509028733
DOIs
StatePublished - Jan 18 2018
Event56th IEEE Annual Conference on Decision and Control, CDC 2017 - Melbourne, Australia
Duration: Dec 12 2017Dec 15 2017

Publication series

Name2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
Volume2018-January

Other

Other56th IEEE Annual Conference on Decision and Control, CDC 2017
CountryAustralia
CityMelbourne
Period12/12/1712/15/17

ASJC Scopus subject areas

  • Decision Sciences (miscellaneous)
  • Industrial and Manufacturing Engineering
  • Control and Optimization

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