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Random adaptive control for cluster synchronization of complex networks with distinct communities
Author(s) -
Tang Ze,
Park Ju H.,
Lee Tae H.,
Feng Jianwen
Publication year - 2016
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.2599
Subject(s) - synchronization (alternating current) , control theory (sociology) , cluster (spacecraft) , bernoulli's principle , realization (probability) , lyapunov stability , lyapunov function , stability (learning theory) , complex network , bernoulli distribution , mathematics , computer science , mathematical optimization , control (management) , topology (electrical circuits) , random variable , engineering , statistics , artificial intelligence , nonlinear system , physics , combinatorics , quantum mechanics , machine learning , programming language , aerospace engineering
Summary In this paper, we investigate the cluster synchronization for complex networks with time‐varying delayed couplings, stochastic disturbance, and non‐identical nodes in different clusters. Based on randomly occurring controllers, some Bernoulli stochastic variables are introduced to describe the controllers, then, a fraction of nodes in clusters, which have direct connections to the other clusters, is controlled, and the states of the whole dynamical networks can be globally forced to the objective cluster states. Sufficient conditions are derived to guarantee the realization of the mean square cluster synchronization pattern for all initial values by means of Lyapunov stability theory, It ô differential formula, and LMI approach. Besides, by designing the randomly occurring adaptive update law, some suitable control gains are obtained. Finally, numerical simulations are also given to demonstrate the effectiveness and validity of the main result. Copyright © 2015 John Wiley & Sons, Ltd.