A multi-weighted coupled neural networks (MWCNNs) model with event-triggered communication is studied here. On the one hand, the passivity of the presented network model is studied by utilising Lyapunov stability theory and some inequality techniques, and a synchronisation criterion based on the obtained output-strict passivity condition of MWCNNs with event-triggered communication is derived. On the other hand, some robust passivity and robust synchronisation criteria based on output-strict passivity of the proposed network with uncertain parameters are presented. At last, two numerical examples are provided to testify the effectiveness of the output-strict passivity and robust synchronisation results.

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Event-triggered communication for passivity and synchronisation of multi-weighted coupled neural networks with and without parameter uncertainties

Synchronization for multiweighted and directly coupled reaction-diffusion neural networks with hybrid coupling via boundary control

Output synchronization analysis and PD control for coupled fractional-order neural networks with multiple weights

This paper mainly addresses the practical consensus problem of nonlinear multi-agent systems modeled by reaction–diffusion equations subject to the bounded external disturbances. Different from the existing consensus control methods associated with spatiotemporal dynamics, the proposed H∞ Neumann boundary controller based on distributed measurement data can guarantee the optimal disturbance attenuation performance under the actuator saturation. Initially, a consensus spatiotemporal error model is constructed by introducing the Kronecker product and equivalent directed graph. Subsequently, a linear matrix inequalities (LMIs)-based sufficient condition is derived by combining the improved Lyapunov-based approach and H∞ norm. Then, an optimization problem is proposed by applying invariant set, such that the consensus errors can converge to a minimized bounded region in the presence of actuator saturation. Finally, comparison simulations on the synchronization of FitzHugh–Nagumo (FHN) model are given to demonstrate the effectiveness of proposed methodology. 

LMI-based H∞ boundary practical consensus control for nonlinear multi-agent systems with actuator saturation.

This essay is devoted to studying H ∞ $\mathcal {H}_\infty$ synchronization problem of directed and switched coupled stochastic delayed neural networks with multi-weights (SCSDNNMWs) via designing a novel event-triggered protocol. The proposed model is based on stochastic delayed neural network with directed coupling, and multiple coupling matrices with switching express intricate and changing communication channels. Since the external disturbances are likely to cause network topologies change, fixed and accurate values of coupling matrices are difficult to obtain, while the above model has more advantages of characterizing this real network. Besides, zero eigenvalue of different coupling matrices are represented by the corresponding normalized left eigenvectors (NLEVec), which is hard to establish yet especially when designing necessary Lyapunov functions. The authors' essay deduces that if the Chebyshev distance among NLEVec of multiple coupling matrices is less than a permissible deviation limit based on a weighted set of these NLEVec, then several event-triggered H ∞ $\mathcal {H}_\infty$ synchronization and synchronization criteria are established. The effectiveness of these results are verified by several given examples. 

Event‐triggered H∞$\mathcal {H}_\infty$ synchronization of directed and switched coupled stochastic delayed neural networks with multi‐weights

Synchronization and control for directly coupled reaction-diffusion neural networks with multiple weights and hybrid coupling

In this article, the passivity and control issues for directed uncertain coupled dynamical networks are solved. The presented model is directly coupled with multiple coupling matrices and parametric uncertainty, while previous literatures of multiweighted networks usually suppose that outer coupling matrices (OMs) are connected, undirected, and certain. The viewpoint of inner coupling matrices (IMs) in this article is added and OMs can be directed and not connected, which is a great improvement on the existing results. First, for all diagonal IMs, considering each dimension separately, we can derive if the weighted combination of multiple OMs for each dimension is strongly connected, then passivity and pinning control rules can be established. In addition, we also discuss the situation that IMs are positive definite but not diagonal. By means of the weighted combination of normalized left eigenvectors (NLEVec) corresponding to zero eigenvalue for multiple coupling matrices, we prove if the Chebyshev distance (Cheb-Dist) among these NLEVec is less than a tolerant deviation interval, then passivity, synchronization, and pinning control criteria are acquired. Moreover, a matter of adaptive coupling strengths is also settled. Examples are provided to verify the validity of established results.

Robust Passivity and Control for Directed and Multiweighted Coupled Dynamical Networks.

This article is dedicated to addressing the generalized decay synchronization problem of directly coupled stochastic dynamic networks with multiple time delays. First, by means of the presentations of the <inline-formula> <tex-math notation="LaTeX">$\psi $ </tex-math></inline-formula>-type function and <inline-formula> <tex-math notation="LaTeX">$\psi $ </tex-math></inline-formula>-type stability, the definitions of decay synchronization <inline-formula> <tex-math notation="LaTeX">$(\psi $ </tex-math></inline-formula>-type synchronization) are introduced. After that, by constructing appropriate feedback controllers and the Lyapunov functional method, we study the decay synchronization for multiple coupled dynamic networks. Moreover, for different coupling matrices, their zero eigenvalues are correspondingly denoted by different normalized left eigenvectors (NLEVec), so it is difficult to establish the functional based on these NLEVec. With the help of the weighted combination of NLEVec for multiple coupling matrices, under the assumption that the Chebyshev gap among NLEVec is less than an allowable deviation interval, some generalized decay (anti-) synchronization conditions are established. Furthermore, we discuss exponential synchronization and polynomial synchronization as special cases, and more relevant criteria are acquired. Examples are provided to verify the effectiveness of those obtained conditions.

Shan-Rang Lin

Papers

Synchronization and control for directly coupled reaction-diffusion neural networks with multiple weights and hybrid coupling

Synchronization for multiweighted and directly coupled reaction-diffusion neural networks with hybrid coupling via boundary control

Robust Passivity and Control for Directed and Multiweighted Coupled Dynamical Networks.

Event‐triggered H∞$\mathcal {H}_\infty$ synchronization of directed and switched coupled stochastic delayed neural networks with multi‐weights

Generalized Decay Synchronization of Directly Coupled Stochastic Dynamic Networks With Multiple Time Delays