Synchronization of delayed neural networks with hybrid coupling via impulsive control

Abstract

The synchronization problem of coupled neural networks via impulsive control is investigated in the present paper. Based on a time varying Lyapunov functional associated with the impulsive time sequence, the delay-dependent criteria in terms of linear matrix inequalities are derived to guarantee the synchronization of the coupled neural networks. The obtained criteria are closely related to both the lower and the upper bound of the adjacent impulsive instant difference. By solving the corresponding linear matrix inequalities, the synchronization criteria can be used to estimate the upper bound of both transmission delay and distributed-delay. The low-dimensional criteria also are obtained for the coupled neural networks with identical nodes. Finally, two examples are given to illustrate the validity of the proposed hybrid control.

Event-triggered passivity and synchronization of coupled reaction–diffusion neural networks with and without time-varying delay

“…Remark 2. Recently, numerous meaningful and significant synchronization results of CNNs have been reported (Cao et al, 2008;Tang et al, 2016;Wang et al, 2017a;Wu and Chen, 2008;Yang and Huang, 2017;Yang et al, 2013;Yu et al, 2019;Zhang and Gao, 2017). Note that CNNs described by a set of ordinary different equations overlook the diffusion phenomena.…”

“…First, we put forward two kinds of models that one is CRDNNs and the other is coupled delayed reactiondiffusion neural networks (CDRDNNs), which are all based on distributed triggering event schemes. Different from the CNNs in previous works (Cao et al, 2008;Knight et al, 2006;Li and Cao, 2016;Lin et al, 2018;Ren et al, 2018;Tang et al, 2016;Wang et al, 2017aWang et al, , 2017bWu and Chen, 2008;Wu et al, 2013;Yang and Huang, 2017;Yang et al, 2013;Yu et al, 2019;Zhang and Gao, 2017;Zheng et al, 2002), reaction-diffusion effects are considered into the current network model, which is more universal and can simulate more real-world networks. 2.…”

“…Some sufficient conditions are established for CRDNNs to realize event-triggered passivity and synchronization. As is well-known, a large number of the traditional synchronization (Cao et al, 2008;Dharani et al, 2017;Tang et al, 2016;Wang and Wu, 2014;Wang et al, 2016Wang et al, , 2017aWang et al, , 2017cWu and Chen, 2008;Yang and Huang, 2017;Yang et al, 2013;Yu et al, 2019;Zhang and Gao, 2017) and passivity (Huang et al, 2018b(Huang et al, , 2019Li and Cao, 2016;Lin et al, 2018;Ren et al, 2017Ren et al, , 2018Wang et al, 2017b;Xu et al, 2016) results are derived for CNs. In contrast to those methods in above-mentioned works, the acquired results in our paper mainly rely on the triggering event mechanism, which can conquer the defects on a continuous method and decrease the redundant transmission of some communication media, especially when information is exchanging.…”

“…To our best knowledge, synchronization is one of the most essential properties of dynamics, and thus, the synchronization problem of CNNs has received great attention and become a research hotspot. In recent years, a good deal of significant and interesting results on this topic has been derived (Cao et al, 2008; Tang et al, 2016; Wang et al, 2017a; Wu and Chen, 2008; Yang and Huang, 2017; Yang et al, 2013; Yu et al, 2019; Zhang and Gao, 2017). In Zhang and Gao (2017), the scholars studied CNNs with time-varying delay, and several synchronization criteria were acquired to realize synchronization based on Lyapunov functional approach.…”

Modeling and parameter learning method for the Hammerstein–Wiener model with disturbance

“…Almost all practical industrial processes have nonlinear characteristics to some extent. 1,2 For decades, many methodologies have been carried out in the field of nonlinear dynamic system modeling and identification, for example, Volterra series, 3 block-oriented nonlinear models, [4][5][6][7][8][9][10][11][12] neural networks, 13,14 support vector machines, 15,16 and Markov jump systems. 17 Among these methodologies, block-oriented nonlinear models have received widespread attention due to their simple structure and excellent modeling ability.…”