TY - GEN
T1 - On convergence rate of a continuous-time distributed self-appraisal model with time-varying relative interaction matrices
AU - Xia, Weiguo
AU - Liu, Ji
AU - Basar, Tamer
AU - Sun, Xi Ming
N1 - The work of Xia was supported in part by the National Natural Science Foundation of China (61603071) and the Fundamental Research Funds for the Central Universities (DUT15RC(3)131). The work of Ba\u015Far was supported in part by Office of Naval Research (ONR) MURI Grant N00014-16-1-2710, and in part by NSF under grant CCF 11-11342.
Weiguo Xia and Xi-Ming Sun are with the School of Control Science and Engineering, Dalian University of Technology, China ({wgxiaseu,sunxm}@dlut.edu.cn). Ji Liu is with the Department of Electrical and Computer Engineering, Stony Brook University, USA ([email protected]). Tamer Bas\u00B8ar is with the Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, USA ([email protected]). The work of Xia was supported in part by the National Natural Science Foundation of China (61603071) and the Fundamental Research Funds for the Central Universities (DUT15RC(3)131). The work of Bas\u00B8ar was supported in part by Office of Naval Research (ONR) MURI Grant N00014-16-1-2710, and in part by NSF under grant CCF 11-11342.
PY - 2017/6/28
Y1 - 2017/6/28
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/85046257303
UR - https://www.scopus.com/pages/publications/85046257303#tab=citedBy
U2 - 10.1109/CDC.2017.8264257
DO - 10.1109/CDC.2017.8264257
M3 - Conference contribution
AN - SCOPUS:85046257303
T3 - 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
SP - 4076
EP - 4081
BT - 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 56th IEEE Annual Conference on Decision and Control, CDC 2017
Y2 - 12 December 2017 through 15 December 2017
ER -