In this paper, the distributed synchronization problem of networks of agent systems with controllers and nonlinearities subject to bernoulli switchings is investigated. Controllers and adaptive updating laws injected ...
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In this paper, the distributed synchronization problem of networks of agent systems with controllers and nonlinearities subject to bernoulli switchings is investigated. Controllers and adaptive updating laws injected in each vertex of networks depend on the state information of its neighborhood. Three sets of bernoulli stochastic variables are introduced to describe the occurrence probabilities of distributed adaptive controllers, updating laws and nonlinearities, respectively. By the Lyapunov functions method, we show that the distributed synchronization of networks composed of agent systems with multiple randomly occurring nonlinearities, multiple randomly occurring controllers, and multiple randomly occurring updating laws can be achieved in mean square under certain criteria. The conditions derived in this paper can be solved by semi-definite programming. Moreover, by mathematical analysis, we find that the coupling strength, the probabilities of the bernoulli stochastic variables, and the form of nonlinearities have great impacts on the convergence speed and the terminal control strength. The synchronization criteria and the observed phenomena are demonstrated by several numerical simulation examples. In addition, the advantage of distributed adaptive controllers over conventional adaptive controllers is illustrated.
In this paper, we study the distributed synchronization and pinning distributed synchronization of stochastic coupled neural networks via randomly occurring control. Two bernoulli stochastic variables are used to desc...
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In this paper, we study the distributed synchronization and pinning distributed synchronization of stochastic coupled neural networks via randomly occurring control. Two bernoulli stochastic variables are used to describe the occurrences of distributed adaptive control and updating law according to certain probabilities. Both distributed adaptive control and updating law for each vertex in a network depend on state information on each vertex's neighborhood. By constructing appropriate Lyapunov functions and employing stochastic analysis techniques, we prove that the distributed synchronization and the distributed pinning synchronization of stochastic complex networks can be achieved in mean square. Additionally, randomly occurring distributed control is compared with periodically intermittent control. It is revealed that, although randomly occurring control is an intermediate method among the three types of control in terms of control costs and convergence rates, it has fewer restrictions to implement and can be more easily applied in practice than periodically intermittent control.
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 co...
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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 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 (c) 2015 John Wiley & Sons, Ltd.
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