Abstract
This paper is devoted to the study of synchronization problems in uncertain dynamical networks with time-delayed nodes and coupling delays. First, a complex dynamical network model with time-delayed nodes and coupling delays is given. Second, for a complex dynamical network with known or unknown but bounded nonlinear couplings, an adaptive controller is designed, which can ensure that the state of a dynamical network asymptotically synchronizes at the individual node state locally or globally in an arbitrary specified network. Then, the Lyapunov-Krasovskii stability theory is employed to estimate the network coupling parameters. The main results provide sufficient conditions for synchronization under local or global circumstances, respectively. Finally, two typical examples are given, using the M-G system as the nodes of the ring dynamical network and second-order nodes in the dynamical network with time-varying communication delays and switching communication topologies, which illustrate the effectiveness of the proposed controller design methods.
Highlights
A complex network refers to a large-scale network with a complex topology and dynamic behavior
This paper studied the adaptive synchronization of uncertain dynamical networks with time-delayed nodes and coupling delays, with known or unknown but bounded nonlinear coupling functions
The parameters of the adaptive controllers can be chosen according to the presented theorems which can stabilize the network to the desired fixed points
Summary
A complex network refers to a large-scale network with a complex topology and dynamic behavior. With the discovery of the small-world effect and scale-free feature of most complex networks, a lot of works have been concentrated on synchronization in small-world networks and scale-free networks [17,18,19,20] In these investigations, an essential requirement is that the structure of the networks and the coupling functions are known beforehand. Yu et al [24] employed a decomposition approach to incorporate the nodes’ inertial effects into the distributed control design for second-order nodes in a dynamical network with communication delays and switching communication topologies. The M-G system is used with the timedelayed nodes in the ring network and second-order nodes in the dynamical network with time-varying communication delays and switching communication topologies.
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