Pinning Impulsive Synchronization of Complex Dynamical Networks

Abstract

In this paper, the problem of pinning impulsive synchronization for complex dynamical networks with directed or undirected but a strongly connected topology is investigated. To remedy this problem, we propose an efficient algorithm to find certain suitable nodes to be controlled via pinning and these selected nodes, in general, could be different at distinct impulsive time instants. The proposed algorithm guarantees the efficiency of the designed pinning impulsive strategy for the global exponential synchronization of state-coupled dynamical networks under an easily-verified condition. In other words, impulsive controllers and an efficient algorithm are designed to control a small fraction of the nodes, which successfully controls the whole dynamical network. Furthermore, we also estimate the upper bound of the number of pinning nodes, which is shown to be closely related to the impulsive intervals. The relationship implies that the required number of pinning nodes, which should be controlled for the successful control of the whole dynamical network, can be greatly reduced by reducing the impulses interval. Finally, simulations of scale-free and small-world networks are given to illustrate the effectiveness of the theoretical results.

Cluster synchronization for directed heterogeneous dynamical networks via decentralized adaptive intermittent pinning control

“…Therefore, it is practically impossible to control a complex network by applying control actions to all nodes [14]. To solve this problem and economize the control cost, pinning control has been proposed and much efforts have been devoted to this research subject [14][15][16][17][18][19][20][21].…”

“…The control action is hence directly exerted only into pinned nodes and propagates to the uncontrolled nodes through the connections among the nodes [20]. Recently, pinning-control scheme has been generalized to investigate cluster synchronization problems for complex dynamical networks with identical or nonidentical nodes [10,[22][23][24][25][26][27][28].…”

Synchronization of delayed neural networks with hybrid coupling via impulsive control

“…The robust impulsive synchronization in chaotic delayed neural networks with uncertainties (Bagheri and Ozgoli, 2016; Ji et al, 2015) has been studied based on the well-known extended Halany inequality and Lyapunov functions. For the CDNs with a strongly connected topology and the CDNs with nonlinear coupling (Lu et al, 2012; Mahdavi et al, 2012), the pinning impulsive control has been introduced according to the error signal of the follower-leader systems. However, the CDNs studied in Mahdavi et al (2012) and Lu et al (2012) are delay-free.…”

“…For the CDNs with a strongly connected topology and the CDNs with nonlinear coupling (Lu et al, 2012; Mahdavi et al, 2012), the pinning impulsive control has been introduced according to the error signal of the follower-leader systems. However, the CDNs studied in Mahdavi et al (2012) and Lu et al (2012) are delay-free.…”

Synchronization Control for Nonlinear Stochastic Dynamical Networks: Pinning Impulsive Strategy

“…Different kinds of effective methods, including adaptive controllers [23], [24], impulsive controllers [25]- [27] and pinning state feedback controllers [19], [20], have been designed for the stabilization and synchronization of complex dynamical networks. In [23], [24], the feedback strength is asymptotically enhanced according to a certain update law for the stabilization and synchronization of dynamical networks.…”