Cluster Synchronization for Interacting Clusters of Nonidentical Nodes via Intermittent Pinning Control

On Pinning Linear and Adaptive Synchronization of Multiple Fractional-Order Neural Networks With Unbounded Time-Varying Delays

In this article, the synchronization of multiple fractional-order neural networks with unbounded time-varying delays (FNNUDs) is investigated. By introducing a pinning linear control, sufficient conditions are provided for achieving the synchronization of multiple FNNUDs via an extended Halanay inequality. Moreover, a new effective adaptive control which applies to the fractional differential equations with unbounded time-varying delays is designed, under which sufficient criteria are presented to ensure the synchronization of multiple FNNUDs. The introduced control in this article is also workable in traditional integer-order neural networks. Finally, the validity of obtained results is demonstrated by a numerical example.

Switching cluster synchronization control of networked harmonic oscillators subject to denial-of-service attacks

This paper is concerned with the average cluster synchronization control problem of networked harmonic oscillators under denial-of-service (DoS) attacks. Different from some existing DoS attack models that often necessitate specific statistical characteristics, only the worse-case duration bound of the DoS attacks is required during the control design procedure, which represents the least a priori knowledge of realistic DoS attacks. Then, a novel switching cluster synchronization control scheme, which leverages a position-based feedback control protocol under a non-small delay and a position velocity-based feedback control protocol with a small delay, is developed such that the above two control protocols are selected based on the occurrence of the DoS attacks. Via formulating the resultant synchronization system as a switched time-delay system, a complete-type Lyapunov-Krasovskii functional (LKF) method is further proposed to establish sufficient controller design criteria associated with the duration and frequency of attacks for both synchronous and asynchronous DoS attacks among clusters. Furthermore, an iterative algorithm is designed to calculate the control gain matrices by solving a set of nonlinear matrix inequalities (NLMIs). Finally, a multi-vehicle cooperative control system is presented to demonstrate the validity of the proposed control scheme.

Almost Surely Exponential Synchronization of Complex Dynamical Networks Under Aperiodically Intermittent Discrete Observations Noise

This article deals with the almost surely exponential synchronization issue for complex dynamical networks (CDNs) under noise control. Different from most of the existing literature, aperiodically intermittent discrete observations noise control is proposed. It is worth noting that the state in noise work time is discretely observed rather than continuously. Meanwhile, some sufficient conditions are presented based on stochastic analytical techniques and the Lyapunov method. Besides, the upper bounds of noise rest rate and the time lag between two consecutive observations are estimated. Moreover, it is clear that CDNs are easier to achieve the almost surely exponential synchronization when noise control gain becomes larger. To demonstrate the effectiveness and feasibility of analytical results, two applications about single-link robot arm systems as well as second-order oscillator systems are given. At the same time, some numerical simulations are exhibited.

Semi-global cluster synchronization for nonlinear systems under fixed and switching topologies

In this paper, the cluster synchronization problem for heterogeneous nonlinear systems with input saturation is studied under both fixed and switching topologies. The distributed feedback controllers are first designed by low gain technique to deal with the input saturation. Sufficient conditions for reaching semi-global cluster synchronization are derived by utilizing the algebraic graph theory, Lyapunov method, and low gain technique. It is shown that the semi-global cluster synchronization problem can be solved by using the proposed synchronization protocols on some preconditions for both fixed and switching topologies. Moreover, under the switching topology, the lower bound of the total activation time for the derived topology with a directed spanning tree is explicitly specified. Finally, some examples are presented to demonstrate the effectiveness of the proposed theories.

Semiglobal Cluster Consensus for Heterogeneous Systems With Input Saturation

In this article, the semiglobal cluster consensus problem is investigated for heterogeneous generic linear systems with input saturation. A general case in a leaderless framework is studied first, and then in order to broaden the scope of application, we consider a special case in which the leader nodes are pinned intermittently. To tackle the above problems, we propose a linear control scheme by using the low-gain feedback technique under the assumptions that each node is asymptotically null controllable and the underlying topology of each cluster (the extended cluster under the intermittent pinning control) has a directed spanning tree. The Lyapunov-based method and the low-gain feedback technique are developed for convergence analysis. It is shown that for both cases, the convergence rate is explicitly specified, which depends on the low-gain parameter and system matrices. Finally, two numerical examples are provided to verify the effectiveness of the theoretical findings.

Synchronization of Coupled Time-Delay Neural Networks With Mode-Dependent Average Dwell Time Switching

In the literature, the effects of switching with average dwell time (ADT), Markovian switching, and intermittent coupling on stability and synchronization of dynamic systems have been extensively investigated. However, all of them are considered separately because it seems that the three kinds of switching are different from each other. This article proposes a new concept to unify these switchings and considers global exponential synchronization almost surely (GES a.s.) in an array of neural networks (NNs) with mixed delays (including time-varying delay and unbounded distributed delay), switching topology, and stochastic perturbations. A general switching mechanism with transition probability (TP) and mode-dependent ADT (MDADT) (i.e., TP-based MDADT switching in this article) is introduced. By designing a multiple Lyapunov-Krasovskii functional and developing a set of new analytical techniques, sufficient conditions are obtained to ensure that the coupled NNs with the general switching topology achieve GES a.s., even in the case that there are both synchronizing and nonsynchronizing modes. Our results have removed the restrictive condition that the increment coefficients of the multiple Lyapunov-Krasovskii functional at switching instants are larger than one. As applications, the coupled NNs with Markovian switching topology and intermittent coupling are employed. Numerical examples are provided to demonstrate the effectiveness and the merits of the theoretical analysis.

Asymptotic and Finite-Time Cluster Synchronization of Coupled Fractional-Order Neural Networks With Time Delay

This article is devoted to the cluster synchronization issue of coupled fractional-order neural networks. By introducing the stability theory of fractional-order differential systems and the framework of Filippov regularization, some sufficient conditions are derived for ascertaining the asymptotic and finite-time cluster synchronization of coupled fractional-order neural networks, respectively. In addition, the upper bound of the settling time for finite-time cluster synchronization is estimated. Compared with the existing works, the results herein are applicable for fractional-order systems, which could be regarded as an extension of integer-order ones. A numerical example with different cases is presented to illustrate the validity of theoretical results.

Quasi-Synchronization of Discrete-Time Lur'e-Type Switched Systems With Parameter Mismatches and Relaxed PDT Constraints

This paper investigates the problem of quasi-synchronization for a class of discrete-time Lur'e-type switched systems with parameter mismatches and transmission channel noises. Different from the previous studies referring to the persistent dwell-time (PDT) switching signals, the average dwell-time (ADT) constraints combined with the PDT are considered simultaneously in this paper to relax the limitation of dwell-time requirements and to improve the flexibility of the PDT switching signal design. By virtue of the semi-time-varying (STV) Lyapunov function, the synchronization criteria for transmitter-receiver systems in a switched version are obtained to satisfy a prescribed synchronization error bound. An estimate of the synchronization error bound is provided via the reachable set approach and, further, an explicit description of the error bounds is given. Then, sufficient conditions on the existence of STV observers are derived with a predetermined error bound, and the corresponding observer gains are calculated via solving a group of linear matrix inequalities. Finally, the effectiveness and validness of the developed theoretical results are demonstrated via a numerical example.

Cluster Synchronization for Neutral Stochastic Delay Networks via Intermittent Adaptive Control

This paper studies the problem of cluster synchronization at exponential rates in both the mean square and almost sure senses for neutral stochastic coupled neural networks with time-varying delay via a periodically intermittent pinning adaptive control strategy. The network topology can be symmetric or asymmetric, with each network node being described by neutral stochastic delayed neural networks. When considering the exponential stabilization in the mean square sense for neutral stochastic delay system, the delay integral inequality approach is used to circumvent the obstacle arising from the coexistence of random disturbance, neutral item, and time-varying delay. The almost surely exponential stabilization is also analyzed with the nonnegative semimartingale convergence theorem. Sufficient criteria on cluster synchronization at exponential rates in both the mean square and almost sure senses of the underlying networks under the designed control scheme are derived. The effectiveness of the obtained theoretical results is illustrated by two examples.

Maximizing synchronizability of duplex networks

We study the synchronizability of duplex networks formed by two randomly generated network layers with different patterns of interlayer node connections. According to the master stability function, we use the smallest nonzero eigenvalue and the eigenratio between the largest and the second smallest eigenvalues of supra-Laplacian matrices to characterize synchronizability on various duplexes. We find that the interlayer linking weight and linking fraction have a profound impact on synchronizability of duplex networks. The increasingly large inter-layer coupling weight is found to cause either decreasing or constant synchronizability for different classes of network dynamics. In addition, negative node degree correlation across interlayer links outperforms positive degree correlation when most interlayer links are present. The reverse is true when a few interlayer links are present. The numerical results and understanding based on these representative duplex networks are illustrative and instructive for building insights into maximizing synchronizability of more realistic multiplex networks.