Passivity and robust synchronisation of switched interval coupled neural networks with time delay

This paper is concerned with passivity and robust synchronisation of switched coupled neural networks with uncertain parameters. First, the mathematical model of switched coupled neural networks with interval uncertain parameters is established, which consists of L modes and switches from one mode to another according to the switching rule. Second, by employing passivity theory and linear matrix inequality techniques, delay-independent and delay-dependent conditions are derived to guarantee the passivity of switched interval coupled neural networks. Moreover, based on the proposed passivity results, global synchronisation criteria can be obtained for switched coupled neural networks with or without uncertain parameters. Finally, an illustrative example is provided to demonstrate the effectiveness of the obtained results.     

Adaptive feedback synchronisation of complex dynamical network with discrete-time communications and delayed nodes

This paper considered the synchronisation of continuous complex dynamical networks with discrete-time communications and delayed nodes. The nodes in the dynamical networks act in the continuous manner, while the communications between nodes are discrete-time; that is, they communicate with others only at discrete time instants. The communication intervals in communication period can be uncertain and variable. By using a piecewise Lyapunov–Krasovskii function to govern the characteristics of the discrete communication instants, we investigate the adaptive feedback synchronisation and a criterion is derived to guarantee the existence of the desired controllers. The globally exponential synchronisation can be achieved by the controllers under the updating laws. Finally, two numerical examples including globally coupled network and nearest-neighbour coupled networks are presented to demonstrate the validity and effectiveness of the proposed control scheme.     

Explicit synchronisation of heterogeneous dynamics networks via three-layer communication framework

This paper addresses the explicit synchronisation of heterogeneous dynamics networks via three-layer communication framework. The main contribution is to propose an explicit synchronisation algorithm, in which the synchronisation errors of all the agents are decoupled. By constructing a three-layer node model, the proposed algorithm removes the assumptions that the topology is fixed and the synchronisation process is coupled. By introducing appropriate assumptions, the algorithm leads to a class of explicit synchronisation protocols based on the states of agents in different layers. It is proved in the sense of Lyapunov that, if the dwell time is larger than a threshold, the explicit synchronisation can be achieved for closed-loop heterogeneous dynamics networks under switching topologies. The results are further extended to the cases in which the switching topologies are only frequently but not always connected. Simulation results are presented with four single-link manipulators to verify the theoretical analysis.     

Synchronisation of complex networks with derivative coupling via adaptive control

This article investigates the synchronisation of complex dynamic networks with derivative coupling and time-varying coupling delay. Based on Lyapunov stability theory, adaptive synchronisation criterion is obtained. The analytical results show that under the designed adaptive controllers, the complex networks with derivative coupling and time-varying coupling delay can realise synchronisation. Furthermore, the coupling matrix is not assumed to be symmetric or irreducible, and the weight configuration matrices can be identified. Numerical examples are provided to demonstrate the effectiveness of the theory.     

Finite-time robust passive control for a class of switched reaction-diffusion stochastic complex dynamical networks with coupling delays and impulsive control

Finite-time boundedness and finite-time passivity for a class of switched stochastic complex dynamical networks (CDNs) with coupling delays, parameter uncertainties, reaction-diffusion term and impulsive control are studied. Novel finite-time synchronisation criteria are derived based on passivity theory. This paper proposes a CDN consisting of N linearly and diffusively coupled identical reaction- diffusion neural networks. By constructing of a suitable Lyapunov–Krasovskii's functional and utilisation of Jensen’s inequality and Wirtinger's inequality, new finite-time passivity criteria for the networks are established in terms of linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. Finally, two interesting numerical examples are given to show the effectiveness of the theoretical results.     

Bounded synchronisation of a time-varying dynamical network with nonidentical nodes

This paper investigates the global bounded synchronisation problem of complex dynamical networks of coupled nonidentical nodes with general time-varying topology through the Lyapunov function and graph theory. Several sufficient conditions in form of scalar inequalities are established so that the global bounded synchronisation of the general dynamical network can be evaluated by the stability of a linear time-varying system and the boundedness of a nonlinear function, both associated with the dynamics of nonidentical nodes. These analytical results are simple yet generic, without assuming the symmetry coupling configuration matrix or calculating their eigenvalues. They can be used to explore synchronisation issues of various complex networks. Numerical simulations show their effectiveness.     

Synchronisation of discrete-time complex networks with randomly occurring uncertainties,nonlinearities and time-delays

This paper deals with the synchronisation problem for an array of coupled complex discrete-time networks with the presence of randomly occurring information. The time-varying delays, parameter uncertainties and nonlinearities enter into the system in a random way and such randomly occurring time-delays, randomly occurring uncertainties and randomly occurring sector-like nonlinearities obey certain mutually uncorrelated Bernoulli-distributed white-noise sequences. By employing direct delay decomposition approach and constructing suitable Lyapunov–Krasovskii functional, sufficient conditions are established to ensure the synchronisation criteria for the complex networks with randomly occurring information in terms of linear matrix inequalities. Finally, in numerical examples, synchronisation of Barabàsi Albert scale-free networks and chaotic synchronisation of Lorenz system are rendered to exemplify the effectiveness and applicability of the proposed results.     

Decentralized dynamic output feedback for globally asymptotic stabilization of a class of dynamic networks

The objective of this paper is to propose an approach to stabilization of a class of dynamic networks with each node being a non-linear system with multiple equilibria. The proposed algorithms, which are developed within the convex optimization framework, employ a decentralized dynamic output feedback structure. Furthermore, an interesting conclusion is reached, in which the stabilization problem for the whole Nn-dimensional dynamic networks can be converted into the simple n-dimensional space in terms of only three LMIs. An application of output stabilization of mutually coupled phase-locked loop networks is used to verify the effectiveness of the proposed methods.     

Synchronisation in an array of spatial diffusion coupled reaction–diffusion neural networks via pinning control

The authors investigate pinning synchronisation for two spatial diffusion coupled reaction–diffusion neural networks under undirected and directed topologies. Combined with stability theory, some inequalities and Lyapunov functional method, several sufficient conditions are derived to assure the synchronisation of the considered networks by designing appropriate pinning controllers. It should be pointed out that a new type of spatial diffusion feedback pinning controller is designed in this paper. The correctness of the obtained results is confirmed by two simulation examples.     

Synchronisation analysis for stochastic T–S fuzzy complex networks with coupling delay

In this paper, we investigated synchronisation problem for stochastic Takagi–Sugeno (T-S) fuzzy complex networks model with discrete and distributed time delays. By constructing a new Lyapunov functional and employing Kronecker product, we developed delay-dependent synchronisation criterions. By applying stochastic analysis techniques, we derive starting conditions for synchronisation complex networks of the addressed with mixed time-varying delays and stochastic disturbances are achieved. A numerical examples are provided to demonstrate the effectiveness and usefulness of the proposed results.     

双环Petersen图互联网络及路由算法

Petersen图由于具有短直径和正则性等特性,因此在并行与分布式计算中具有良好的性能.基于双环结构,构造了一个双环Petersen图互联网络DLCPG(k).同时,分别设计了DLCPG(k)上的单播、广播和容错路由算法.证明了DLCPG(k)不但具有良好的可扩展性、短的网络直径和简单的拓扑结构等特性,而且对于10k个节点组成的互联网络,DLCPG(k)还具有比二维Torus以及RP(k)互联网络更小的直径和更优越的可分组性.另外,还证明了其上的单播、广播路由算法的通信效率与RP(k)上的单播和广播路由算法的通信效率相比均有明显的提高.仿真实验表明,新的容错路由算法也具有良好的容错性能.     

Pinning exponential synchronisation and passivity of coupled delayed reaction–diffusion neural networks with and without parametric uncertainties

In this paper, we focus on the pinning exponential synchronisation and passivity of coupled reaction–diffusion neural networks (CRDNNs) with and without parametric uncertainties, respectively. On the one hand, with the help of designed nonlinear pinning controllers and Lyapunov functional method, sufficient conditions are established to let the CRDNNs with hybrid coupling and mixed time-varying delays realise exponential synchronisation and passivity. On the other hand, considering that the external perturbations may lead the reaction–diffusion neural networks (RDNNs) parameters to containing uncertainties, the robust pinning exponential synchronisation and robust pinning passivity for coupled delayed RDNNs with parametric uncertainties are investigated by designing appropriate pinning control strategies. Finally, the effectiveness of the theoretical results are substantiated by the two given numerical examples.     

Synchronisation of singular complex networks with actuator saturation and randomly occurring time-delay

In this paper, we aim at addressing the synchronisation of singular complex networks with actuator saturation and randomly occurring time-delay. Based on Lyapunov–Krasovskii approach, delay-dependent condition is first derived such that the corresponding singular complex networks are mean-square synchronisation via the Wirtinger-based inequality and linear matrix inequalities (LMIs) technology. The delay information exchanges occur in a random way. Then the feedback controllers are then designed as well as the domain of attraction by an optimisation problem. Finally, the illustrate examples are utilised to demonstrate the effectiveness of the obtained results.     

Synchronisation of complex dynamical networks with different dynamics of nodes via decentralised dynamical compensation controllers

This paper investigates the synchronisation of nonlinear coupled complex dynamical networks with different nonlinear nodes and different orders by using decentralised dynamical compensation controllers. We propose a dynamical network mathematical model with similar nonlinear nodes, whose dimensions are different. For this kind of network model, the decentralised dynamical compensation controllers are designed for the state synchronisation of the coupled nodes. In addition, the synchronisation manifold is defined as an invariant manifold, which is regarded as the generalised case of dynamical networks with the same nodes’ dynamics. Furthermore, some stability criteria for the synchronisation are derived by means of rigorous theoretical analysis. Finally, numerical examples are presented to verify the effectiveness of the obtained theoretical results.     

Lower Bounds for Dynamic Tree Embedding in Bipartite Networks

There are many parallel computations that are tree structured. The structure of a tree is usually unpredictable at compiler-time; the tree grows gradually during the course of a computation. The dynamic tree embedding problem is to distribute the processes of a parallel computation over processors in a parallel computer such that processors perform roughly the same amount of computation, and that communicating processes are assigned to processors that are close to each other. In this paper, we establish lower bounds for the performance ratio of dynamic tree embedding in bipartite static networks, including numerous important networks such asn-dimensional meshes,n-dimensional tori,k-aryn-cubes, cube-connected cycles, and butterflies. Our lower bounds are obtained from both tree and network properties and are applicable to a general class of dynamic tree embedding algorithms.     

A programming model for BSP with partitioned synchronisation

A BSP superstep is a distributed computation comprising a number of simultaneously executing processes which may generate asynchronous messages. A superstep terminates with a barrier which enforces a global synchronisation and delivers all ongoing communications. Multilevel supersteps can utilise barriers in which subsets of processes, interacting through shared memories, are locally synchronised (partitioned synchronisation). In this paper a state-based semantics, closely related to the classical sequential programming model, is derived for distributed BSP with partitioned synchronisation.     

Global synchronised regions of linearly coupled Lur'e systems

This article addresses the global synchronisation problem of a network of coupled Lur'e systems from the perspective of global synchronised region. A decomposition approach is proposed to convert the synchronisation of high-dimensional Lur'e networks into the test of a set of matrix inequalities whose dimensions are the same as a single Lur'e node. The notion of global synchronised region is then introduced and analysed. A necessary and sufficient condition is derived for the existence of the inner-linking matrix to guarantee a desirable unbounded synchronised region. A multi-step design procedure is given for constructing such an inner-linking matrix, which maintains a favourable decoupling property. Furthermore, the global H _∞ synchronised region is characterised for evaluating the performance of a Lur'e network subject to external disturbances. The effectiveness of the theoretical results is demonstrated through a network of Chua's circuits.     

Distributed control of cluster synchronisation in networks with randomly occurring non-linearities

This paper is concerned with the issue of mean square cluster synchronisation in complex networks, which consist of non-identical nodes with randomly occurring non-linearities. In order to guarantee synchronisation, distributed controllers depending on the information from the neighbours in the same cluster are applied to each node, meanwhile, the control gains are supposed to be updated according to the given laws. Based on the Lyapunov stability theory, the sufficient synchronisation conditions are derived and proved theoretically. Finally, a numerical example is presented to demonstrate the effectiveness of the results.     

Stabilisation of SDEs and applications to synchronisation of stochastic neural network driven by G-Brownian motion with state-feedback control

Li, X., Lin, X., and Lin, Y. [(2016). Lyapunov-type conditions and stochastic differential equations driven by G-Brownian motion. Journal of Mathematicase Analysis and Applications, 439, 235–255] proposed the sufficient conditions for the exponential instability to stochastic differential equations driven by G-Brownian motion (G-SDEs, in short). A natural question is whether we can design a controller to make G-SDEs be stable. By means of the G-Lyapunov function, we design a state-feedback controller to stabilise the system. In addition, applications to stabilisation and synchronisation of Hopfield neural networks driven by G-Brownian motion (G-HNNs, in short) and examples are proposed to illustrate the obtained results.     

Robust pinning control of heterogeneous complex networks with jointly connected topologies and time-varying parametric uncertainty

The pinning/leader control problems provide the design of the leader or pinning controller in order to guide a complex network to a desired trajectory or target (synchronisation or consensus). Let a time-invariant complex network, pinning/leader control problems include the design of the leader or pinning controller gain and number of nodes to pin in order to guide a network to a desired trajectory (synchronization or consensus). Usually, lower is the number of pinned nodes larger is the pinning gain required to assess network synchronisation. On the other side, realistic application scenario of complex networks is characterised by switching topologies, time-varying node coupling strength and link weight that make hard to solve the pinning/leader control problem. Additionally, the system dynamics at nodes can be heterogeneous. In this paper, we derive robust stabilisation conditions of time-varying heterogeneous complex networks with jointly connected topologies when coupling strength and link weight interactions are affected by time-varying uncertainties. By employing Lyapunov stability theory and linear matrix inequality (LMI) technique, we formulate low computationally demanding stabilisability conditions to design a pinning/leader control gain for robust network synchronisation. The effectiveness of the proposed approach is shown by several design examples applied to a paradigmatic well-known complex network composed of heterogeneous Chua's circuits.