Pinning synchronization of hybrid-coupled directed delayed dynamical network via intermittent control

Abstract

This paper concerns the problem of exponential synchronization for a class of general delayed dynamical networks with hybrid coupling via pinning periodically intermittent control. Both the internal delay and coupling delay are taken into account in the network model. Meanwhile, the transmission delay and self-feedback delay are involved in the delayed coupling term. By establishing a new differential inequality, several simple and useful exponential synchronization criteria are derived analytically. It is shown that the controlled synchronization state can vary in comparison with the conventional synchronized solution, and the degree of the node and the inner delayed coupling matrix play important roles in the controlled synchronization state. By choosing different inner delayed coupling matrices and the degrees of the node, different controlled synchronization states can be obtained. Furthermore, the detail pinning schemes deciding what nodes should be chosen as pinned candidates and how many nodes are needed to be pinned for a fixed coupling strength are provided. The simple procedures illuminating how to design suitable intermittent controllers in real application are also given. Numerical simulations, including an undirected scale-free network and a directed small-world network, are finally presented to demonstrate the effectiveness of the theoretical results.

Exponential cluster synchronization of hybrid-coupled impulsive delayed dynamical networks: average impulsive interval approach

“…In reality, due to the finite speeds of transmission and spreading as well as traffic congestion, time delay often occurs in the process of information storage and transmission in dynamical networks, and it can cause instability, oscillation or bad system performance [9,[19][20][21][22][23][24][25][26][27][28][29][30][31]. Therefore, it is necessary to study the effect of time delay on synchronization of dynamical networks.…”

“…Generally, there are two types of time delays in dynamical networks. One is internal delay occurring inside the dynamical node [9,[19][20][21][22][23]. The other is coupling delay caused by the exchange of information between dynamical nodes [21][22][23][24][25][26][27][28][29][30][31].…”

Adaptive exponential lag synchronization for neural networks with mixed delays via intermittent control

“…A numerical example is finally provided to demonstrate the effectiveness of the proposed control methodology. The main contributions of this paper can be outlined as follows: (1) different from the periodically intermittent control adopted in previous works [12,13,[28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43], here the adaptive intermittent control is nonperiodic with non-fixed both control period and control width, which extends the intermittent control strategy's application scope; (2) unlike in the references [39][40][41]50], the candidate Lyapunov function introduced in this paper is piecewise continuous, and then by means of which, some criteria ensuring globally exponential lag synchronization are established; (3) the derived theoretical results indicate that the lag synchronization criteria are related to the control rates rather than the control periods, which is propitious to selecting the control periods in practical applications.…”

“…Intermittent control, as a discontinuous control method, has been adopted in engineering fields in view of its convenient implementation in engineering control [33][34][35][36][37][38]. Recently, an intermittent control scheme with fixed both control period and control width, namely periodically intermittent control scheme, has been developed to study the synchronization problem for chaotic systems as well as dynamical networks; see [12,13,[28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43] and references cited therein. However, in practical applications, the requirement that both control period and control width be fixed is evidently unreasonable.…”

Intermittent Control for Cluster-Delay Synchronization in Directed Networks

“…During the past decades, many external control strategies have been carried out to synchronize complex networks, such as adaptive control [14,15], impulsive control [16], sliding 2 Complexity mode control [17], pinning control [18][19][20], sliding mode control [21], and intermittent control [22,23]. Those control strategies have been widely investigated and used in many network control problems.…”