Pinning cluster synchronization in an array of coupled neural networks under event-based mechanism

Event-Triggered Cluster Consensus of Multi-Agent Systems via a Modified Genetic Algorithm

This article is concerned with the event-triggered output feedback cluster consensus of leader-following multi-agent systems (MASs) under limited communication resources. Specifically, the distributed agents are divided into several clusters to accomplish different collective tasks under diverse intracluster and intercluster communications. First, to alleviate excessive communication resource consumption, two sampled-data-based event-triggered schemes are developed to distinguish agent-to-agent communications within clusters and between clusters. Based on these schemes, an event-based cluster consensus control protocol is proposed to solve the problem. Then, sufficient criteria on asymptotic stability of the resulting closed-loop system are derived and expressed in terms of matrix inequalities. It is noteworthy that the derived criteria for controller design are nonlinear and nonconvex with respect to the output feedback control gains and triggering parameters. To handle this issue, a modified genetic algorithm (MGA) with multiple subpopulations is proposed, where the subpopulations are independent of each other. The key feature of the designed MGA lies in that the fitness value is described as an accumulation of initial value and weighing value of each matrix inequality. Finally, an application of satellite formation flying is exemplified to demonstrate the effectiveness of the derived theoretical results.

Finite-time cluster synchronization for complex dynamical networks under FDI attack: A periodic control approach

In this paper, the finite-time cluster synchronization problem is addressed for complex dynamical networks (CDNs) with cluster characteristics under false data injection (FDI) attacks. A type of FDI attack is taken into consideration to reflect the data manipulation that controllers in CDNs may suffer. In order to improve the synchronization effect while reducing the control cost, a new periodic secure control (PSC) strategy is proposed in which the set of pinning nodes changes periodically. The aim of this paper is to derive the gains of the periodic secure controller such that the synchronization error of the CDN remains at a certain threshold in finite time with the presence of external disturbances and false control signals simultaneously. Through considering the periodic characteristics of PSC, a sufficient condition is obtained to guarantee the desired cluster synchronization performance, based on which the gains of the periodic cluster synchronization controllers are acquired by resolving an optimization problem proposed in this paper. A numerical case is carried out to validate the cluster synchronization performance of the PSC strategy under cyber attacks.

Cluster Synchronization of Coupled Neural Networks With Lévy Noise via Event-Triggered Pinning Control

Cluster synchronization means that all multiagents are divided into different clusters according to the equations or roles of nodes in a complex network, and by designing an appropriate algorithm, each cluster can achieve synchronization to a certain value or an isolated node. However, the synchronization values between different clusters are different. With a feedback controller based on the calculation of the control input value and a trigger condition leading to the updating instants, this article introduces the trigger mechanism and designs a new data sampling strategy to achieve cluster synchronization of the coupled neural networks (CNNs), which reduces the number of updates of the controller, thereby reducing unnecessary waste of limited resources. In addition, an example proposes a synchronization algorithm and gives iterative procedures to calculate the trigger instants and prove the validity of the theoretical results.

Pinning Impulsive Synchronization of Stochastic Delayed Neural Networks via Uniformly Stable Function

This article investigates the synchronization of stochastic delayed neural networks under pinning impulsive control, where a small fraction of nodes are selected as the pinned nodes at each impulsive moment. By proposing a uniformly stable function as a new tool, some novel mean square decay results are presented to analyze the error system obtained from the leader and the considered neural networks. For the divergent error system without impulsive effects, the impulsive gains of pinning impulsive controller can admit destabilizing impulse and the number of destabilizing impulse may be infinite. However, if the error system without impulsive effects is convergent, to achieve the synchronization of the stochastic neural networks, the growth exponent of the product of impulsive gains can not exceed some positive constant. It is shown that the obtained results increase the flexibility of the impulsive gains compared with the existing results. Finally, a numerical example is given to illustrate the practicality of synchronization criteria.

Finite-/Fixed-Time Synchronization of Delayed Coupled Discontinuous Neural Networks With Unified Control Schemes

In this article, it addresses the problem of finite-/fixed-time synchronization of delayed coupled discontinuous neural networks in the unified framework. To achieve the finite-/fixed-time synchronization and precise estimations of setting time, two novel different kinds of controllers are established, in which one is switching. Then, based on the finite-/fixed-time theorem and Lyapunov function theory, some useful criteria are obtained to select suitable controllers' parameters, which can guarantee error systems converge in the finite time/fixed time with respect to coupled neural networks. Moreover, corresponding estimations of the setting time are also provided. Finally, two numerical examples are introduced to show the effectiveness of the proposed control protocols.

Exponential quasi-synchronization of coupled delayed memristive neural networks via intermittent event-triggered control

Firstly, an intermittent event-triggered control (IETC), as a combination of intermittent control and event-triggered control, is proposed. Then, the quasi-synchronization problem of coupled memristive neural networks with time-varying delays (CDMNN) is discussed under this IETC. To include more of the existing work, aperiodic intermittent control and event-triggered control with combined measurement errors are adopted in the IETC. Under the IETC, it is shown that Zeno behavior cannot be exhibited for CDMNN. At the same time, two new differential inequalities are established, and some simple and practical criteria for CDMNN quasi-synchronization and synchronization are obtained by using these inequalities. In the obtained results, synchronization is a spatial case of quasi-synchronization, and the activation functions of DMNN do not need to be bounded. Finally, a numerical example and some simulations are provided to test the results in theoretical analysis.

Recent Advances on Dynamical Behaviors of Coupled Neural Networks With and Without Reaction-Diffusion Terms

Recently, the dynamical behaviors of coupled neural networks (CNNs) with and without reaction-diffusion terms have been widely researched due to their successful applications in different fields. This article introduces some important and interesting results on this topic. First, synchronization, passivity, and stability analysis results for various CNNs with and without reaction-diffusion terms are summarized, including the results for impulsive, time-varying, time-invariant, uncertain, fuzzy, and stochastic network models. In addition, some control methods, such as sampled-data control, pinning control, impulsive control, state feedback control, and adaptive control, have been used to realize the desired dynamical behaviors in CNNs with and without reaction-diffusion terms. In this article, these methods are summarized. Finally, some challenging and interesting problems deserving of further investigation are discussed.

Nonfragile Finite-Time Synchronization for Coupled Neural Networks With Impulsive Approach

This article addresses the problem of the average stochastic finite-time synchronization (ASFTS) for a set of coupled neural networks (NNs) with energy-bounded noises. Due to the channel capacity constraint, the impulsive approach is introduced so as to cut down the communication times among the leader NNs and the follower NNs. Then, a nonfragile controller is designed to improve the robustness of the controller with randomly occurred uncertainty. The sufficient conditions that guarantee the ASFTS of the coupled NNs and the leader NNs are achieved. The boundary of the synchronization error is also obtained by constructing the monotonic increasing functions. Finally, the controller gains are given based on the derived conditions, and their effectiveness is illustrated by a numerical example.

Partial-Neurons-Based Passivity-Guaranteed State Estimation for Neural Networks With Randomly Occurring Time Delays

In this brief, the partial-neurons-based passivity-guaranteed state estimation (SE) problem is examined for a class of discrete-time artificial neural networks with randomly occurring time delays. The measurement outputs available utilized for the SE are allowed to be available only at a fraction of neurons in the networks. A Bernoulli-distributed random variable is employed to characterize the random nature of the occurrence of time delays. By resorting to the Lyapunov-Krasovskii functional method as well as the stochastic analysis technique, sufficient criteria are provided for the existence of the desired state estimators ensuring the estimation error dynamics to achieve the asymptotic stability in the mean square with a guaranteed passivity performance level. In addition, the parameterization of the estimator gain is acquired by solving a convex optimization problem. Finally, the validity of the obtained theoretical results is illustrated via a numerical simulation example.

Synchronization of the Networked System With Continuous and Impulsive Hybrid Communications

Many networked systems display some kind of dynamics behaving in a style with both continuous and impulsive communications. The cooperation behaviors of these networked systems with continuous connected or impulsive connected or both connected topologies of communications are important to understand. This paper is devoted to the synchronization of the networked system with continuous and impulsive hybrid communications, where each topology of communication mode is not connected in every moment. Two kind of structures, i.e., fixed structure and switching structures, are taken into consideration. A general concept of directed spanning tree (DST) is proposed to describe the connectivity of the networked system with hybrid communication modes. The suitable Lyapunov functions are constructed to analyze the synchronization stability. It is showed that for fixed topology having a jointly DST, the networked system with continuous and impulsive hybrid communication modes will achieve asymptotic synchronization if the feedback gain matrix and the average impulsive interval are properly selected. The results are then extended to the switching case where the graph has a frequently jointly DST. Some simple examples are then given to illustrate the derived synchronization criteria.

Delay-Distribution-Dependent H∞ State Estimation for Discrete-Time Memristive Neural Networks With Mixed Time-Delays and Fading Measurements

This paper addresses the H _∞ state estimation issue for a sort of memristive neural networks in the discrete-time setting under randomly occurring mixed time-delays and fading measurements. The main purpose of the addressed issue is to propose a state estimator design algorithm that ensures the error dynamics of the state estimation to be stochastically stable with a prespecified H _∞ disturbance attenuation index. We put forward certain switching functions to account for the discrete-time yet state-dependent characteristics of the memristive connection weights. By resorting to the robust analysis theory and the Lyapunov-functional analysis theory, we derive some sufficient conditions to guarantee the desired estimation performance. The derived sufficient conditions rely not only on the size of discrete time-delays and the probability distribution law of the distributed time-delays but also on the statistics information of the coefficients of the adopted Rice fading model. Based on the established existence conditions, the gain matrices of the desired estimator are obtained by means of the feasibility of a set of matrix inequalities that can be checked efficiently via available software packages. Finally, the numerical simulation results are provided to show the validity of the main results.

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.

Event/Self-Triggered Control for Leader-Following Consensus Over Unreliable Network With DoS Attacks

This paper investigates the leader-following consensus issue with event/self-triggered schemes under an unreliable network environment. First, we characterize network communication and control protocol update in the presence of denial-of-service (DoS) attacks. In this situation, an event-triggered communication scheme is first proposed to effectively schedule information transmission over the network possibly subject to malicious attacks. In this communication framework, synchronous and asynchronous updated strategies of control protocols are constructed to achieve leader-following consensus in the presence of DoS attacks. Moreover, to further reduce the cost induced by event detection, a self-triggered communication scheme is proposed in which the next triggering instant can be determined by computing with the most updated information. Finally, a numerical example is provided to verify the effectiveness of the proposed communication schemes and updated strategies in the unreliable network environment.

Synchronization control of quaternion-valued memristive neural networks with and without event-triggered scheme

In this paper, the real-valued memristive neural networks (MNNs) are extended to quaternion field, a new class of neural networks named quaternion-valued memristive neural networks (QVMNNs) is then established. The problem of master-slave synchronization of this type of networks is investigated in this paper. Two types of controllers are designed: the traditional feedback controller and the event-triggered controller. Corresponding synchronization criteria are then derived based on Lyapunov method. Moreover, it is demonstrated that Zeno behavior can be avoided in case of the event-triggered strategy proposed in this work. Finally, corresponding simulation examples are proposed to demonstrate the correctness of the proposed results derived in this work.

An Event-Triggered Pinning Control Approach to Synchronization of Discrete-Time Stochastic Complex Dynamical Networks

This paper is concerned with the synchronization analysis and control problems for a class of nonlinear discrete-time stochastic complex dynamical networks (CDNs) consisting of identical nodes. The discrete-time stochastic dynamical networks under consideration are quite general that account for asymmetric coupling configuration, nonlinear inner coupling structures as well as nonidentical exogenous disturbances. By resorting to both the error bound and the synchronization probability, a notion of quasi-synchronization in probability is first introduced to assess the synchronization performance of the addressed CDNs. An event-triggered pinning feedback control strategy is adopted to control a small fraction of the network nodes with hope to reduce the frequency of updating and communication in the control process while preserving the desired dynamical behaviors of the controlled networks. By using the Lyapunov function method and the stochastic analysis techniques, a general framework is established within which the problems of dynamics analysis and controller synthesis are solved for the closed-loop stochastic dynamical networks. Two numerical examples and their simulations are presented to illustrate the effectiveness and the usefulness of our theoretical results.

Swarming Behavior of Multiple Euler-Lagrange Systems With Cooperation-Competition Interactions: An Auxiliary System Approach

In this paper, the swarming behavior of multiple Euler-Lagrange systems with cooperation-competition interactions is investigated, where the agents can cooperate or compete with each other and the parameters of the systems are uncertain. The distributed stabilization problem is first studied, by introducing an auxiliary system to each agent, where the common assumption that the cooperation-competition network satisfies the digon sign-symmetry condition is removed. Based on the input-output property of the auxiliary system, it is found that distributed stabilization can be achieved provided that the cooperation subnetwork is strongly connected and the parameters of the auxiliary system are chosen appropriately. Furthermore, as an extension, a distributed consensus tracking problem of the considered multiagent systems is discussed, where the concept of equi-competition is introduced and a new pinning control strategy is proposed based on the designed auxiliary system. Finally, illustrative examples are provided to show the effectiveness of the theoretical analysis.

Event-Triggered Cluster Consensus of Leader-Following Linear Multi-Agent Systems

This paper is concerned with cluster consensus of linear multi-agent systems via a distributed event-triggered control scheme. Assume that agents can be split into several clusters and a leader is associated with each cluster. Sufficient conditions are derived to guarantee the realization of cluster consensus by a feasible event-triggered controller if the network topology of each cluster has a directed spanning tree and the couplings within each cluster are sufficiently strong. Further, positive inner-event time intervals are ensured for the proposed event-triggered strategy to avoid Zeno behaviors. Finally, a numerical example is given to illustrate the effectiveness of the theoretical results.

On Group Synchronization for Interacting Clusters of Heterogeneous Systems

This paper investigates group synchronization for multiple interacting clusters of nonidentical systems that are linearly or nonlinearly coupled. By observing the structure of the coupling topology, a Lyapunov function-based approach is proposed to deal with the case of linear systems which are linearly coupled in the framework of directed topology. Such an analysis is then further extended to tackle the case of nonlinear systems in a similar framework. Moreover, the case of nonlinear systems which are nonlinearly coupled is also addressed, however, in the framework of undirected coupling topology. For all these cases, a consistent conclusion is made that group synchronization can be achieved if the coupling topology for each cluster satisfies certain connectivity condition and further, the intra-cluster coupling strengths are sufficiently strong. Both the lower bound for the intra-cluster coupling strength as well as the convergence rate are explicitly specified.