Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 64, Issue 5, Pages 1874-1889Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2018.2867257
Keywords
Terms-Consensus; linear systems; multiagent systems; signed network; stochastic approximation (SA)
Funding
- U.S. Army Research Laboratory
- U.S. Army Research Office [W911NF-15-1-0577]
- National Natural Science Foundation of China [91427304, 61673373, 11688101]
- National Key Basic Research Program of China (973 program) [2014CB845301/2/3]
- Leading research projects of Chinese Academy of Sciences [QYZDJ-SSW-JSC003]
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This paper studies linear stochastic approximation (SA) algorithms and their application to multiagent systems in engineering and sociology. As main contribution, we provide necessary and sufficient conditions for convergence of linear SA algorithms to a deterministic or random final vector. We also characterize the system convergence rate, when the system is convergent. Moreover, differing from non-negative gain functions in traditional SA algorithms, this paper considers also the case when the gain functions are allowed to take arbitrary real numbers. Using our general treatment, we provide necessary and sufficient conditions to reach consensus and group consensus for first-order discrete-time multiagent system over random signed networks and with state-dependent noise. Finally, we extend our results to the setting of multidimensional linear SA algorithms and characterize the behavior of the multidimensional Friedkin-Johnsen model over random interaction networks.
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