Passivity of Directed and Undirected Complex Dynamical Networks With Adaptive Coupling Weights

Abstract

A complex dynamical network consisting of N identical neural networks with reaction-diffusion terms is considered in this paper. First, several passivity definitions for the systems with different dimensions of input and output are given. By utilizing some inequality techniques, several criteria are presented, ensuring the passivity of the complex dynamical network under the designed adaptive law. Then, we discuss the relationship between the synchronization and output strict passivity of the proposed network model. Furthermore, these results are extended to the case when the topological structure of the network is undirected. Finally, two examples with numerical simulations are provided to illustrate the correctness and effectiveness of the proposed results.

Pinning synchronization of fractional‐order complex networks with adaptive coupling weights

“…On the other hand, adaptive coupling has been considered in integer-order networks with reaction-diffusion terms. 14,23 However, until now, very few literature are reported on the pinning synchronization of fractional-order complex networks with adaptive coupling weights. 30 In the work of Ding et al, 30 the indirect network topology is considered and only the weights corresponding to a subset of nodes are adaptive.…”

“…7,18,20 Meanwhile, in some practical scenario, they are needed to be dynamically tuned based on the changes of environment or network itself. 21,22 In the work of Wang et al, 14 the pining synchronization is addressed for reaction-diffusion neural networks under adaptive coupling strength, whereas the other work of Wang et al 23 designs the adaptive coupling weights to ensure the passivity of the considered complex network. However, until now, the adaptive coupling weights in fractional-order complex networks are rare to report, which is the main concern in our work.…”

Consensus Problem with a Reference State for Fractional‐Order Multi‐Agent Systems

“…To study the convergence speeds of consensus by using control laws (10) and (16), we just need to consider the error systems (14) and (18) respectively. According to the Theorem III.2, we just need to compare the largest eigenvalues of matrix −M and −(M + M).…”

“…After that, some theoretical results have been established, and many external limited conditions [10][11][12][13] have been considered, for example external disturbance, model uncertainties, time delay. At the same time, various consensus control laws [14][15][16][17][18] have been designed depending on different conditions and technologies.…”

Passivity and Synchronization of Coupled Different Dimensional Delayed Reaction-Diffusion Neural Networks with Dirichlet Boundary Conditions

“…Unfortunately, the passivity results in aforementioned studies [26][27][28][29][30][31][32][33] are based on the case that the dimension of input is identical with output. As far as we know, only few scholars have addressed the problem of passivity for the network with nonidentical dimensional output and input [34][35][36]. e authors in [34] established some conditions for ensuring that the CRDNNs with the input and output in different dimensions achieve passivity.…”