This paper is concerned with the mean-square synchronization issue of the coupled neural networks (CNNs) subject to deception attacks, where the saturation constraint on impulsive control signal is adequately taken into account. To compensate the effect of deception attacks, a hybrid event-triggered mechanism is developed and a minimum inter-event interval is introduced simultaneously to avoid the Zeno phenomena. Under deception attacks, sufficient conditions to guarantee the achievement of the mean-square exponentially synchronization for the CNNs are presented with a novel method combined with mathematical induction, polyhedral representation of saturation nonlinearity, proof by contradiction, which address the actuator saturation in discrete-time control signals effectively. Meanwhile, in consideration of different impulsive effects, three optimization problems are constructed for the sake of acquiring the maximum estimation of the domain of attraction, the feasible maximal impulsive interval and the admissible feasible minimum impulsive interval, respectively. Finally, two numerical simulations are carried out to illustrate the validity of the proposed theoretical analysis. Note to Practitioners—In the engineering and industry, the synchronization control of CNNs exists in many different fields, including image processing, fluid dynamics, and secure communication. The control signals and plant information are transmitted over communication network which is vulnerable to deception attacks. To save communication resources and compensate the effect of deception attacks, a hybrid event-triggered scheme is proposed. Simultaneously, the synthesis of impulse effects and actuator saturation are considered to make results more practical. In addition, three optimization problems are proposed to derive the maximum estimation of the domain of attraction, some related parameters selection of event-triggered scheme.

This paper studies the exponential synchronization issue of complex dynamic networks (CDNs) under dual-channel attacks by utilizing distributed delayed pinning impulsive control strategy. A dual-channel attack model with differentiated node attack probabilities is established by simultaneously considering replacement attacks in the sensor-to-controller channels and injection attacks in the controller-to-actuator channels. Within this approach, The novel concept of average delayed impulsive gains has been introduced to holistically measure the combined temporal influence of impulsive delays and gains across time. Furthermore, by use of the formula for the variation of parameters and applying comparison principle to hybrid delayed impulses, sufficient conditions for achieving the exponential synchronization of the networks are ultimately derived. Finally, numerical simulations verify the effectiveness and superiority of the proposed control strategy.

This article is devoted to dealing with the secure synchronization for complex networks suffering from deception attacks via impulsive control. Notably, false data would be injected in a fully distributed manner with various attack signals diffusing in node-to-node communication channels. The controlled error system is implicitly represented in the form of tracking errors within the error conjunction matrix. In consideration of the risk that synchronizing impulses may be transformed into impulsive disturbances due to malicious attacks, an extended definition of average impulsive gain is introduced to describe the hybrid impulse sequence containing diametrically opposed functions. Moreover, a self-triggered mechanism integrating memory characteristic is built to regulate impulse activations. By leveraging historical temporal data, the issue of active attacks induced by activation impulse signals is effectively circumvented. With the Lyapunov stability theorem, the error conjunction matrix, and the comparison system-based method, sufficient conditions for secure synchronization could be obtained. The given simulation examples show that the self-triggered impulsive controller could perform well under the attack scenarios.

This article considers the saturated distributed impulsive local exponential synchronization (LES) issue for directed coupled neural networks (CNNs) with proportional delay and distributed delay under the impulsive time window (ITW) scheme. By utilizing a modified compact convex hull representation of the saturation nonlinearity, the extended parameter variation formula, and the proportional delayed impulsive comparison principle, sufficient conditions for the local exponential synchronization (LES) of the CNNs subject to actuator saturation are obtained within the domain of attraction (DOA). Based on these conditions, an optimization problem constructed by transformed linear matrix inequality (LMI) constraints is formulated to determine the impulsive control gain for enlarging the estimation of DOA as much as possible with a predetermined exponential convergence rate. Ultimately, a numerical simulation is exhibited to illustrate the feasibility and validity of the theoretical results.

This paper investigates the cosensus for a class of nonlinear multi-agent systems. As one of the boundless delays, proportional delay is introduced by considering the existence of tremendous amount of parallel information transfer paths with different axon sizes or lengths. To better reduce the complexity of analysis, three different parameter functions are constructed to deal with the proportional delayed systems. In view of the limited bandwidth and fully distributed architecture of agents in most practical applications, the distributed edge-based self-triggering impulsive (DEBSTI) controller is elaborately designed to eliminate the continuous monitoring, high control costs and global information transmission. Sufficient conditions are derived for achieving the consensus globally and exponentially by utilizing the methods of parameter variation, comparison principle, and average impulsive interval. In addition, the Zeno behavior could be avoided. Furthermore, a larger value range for the impulsive-effect-related parameter taking is obtained by considering the diverse functions of the impulses. Correspondingly, different convergence rates based on different ranges are calculated precisely. Finally, twenty one-link manipulators actuated by twenty DC motors are discussed in numerical simulation to demonstrate the effectiveness of the proposed results.Note to Practitioners—Nonlinear multi-agent systems could be applied to simulate large-scale systems like UAV formation and one-link manipulator with revolute joints. By considering the continuous monitoring, high control costs and global information transmission, the DEBSTI controller is skillfully designed. In view of the tremendous amount of parallel information transfer paths with different axon sizes or lengths, the proportional delay is taken into consideration to make results more practical based on three different parameter functions. Moreover, different impulsive functions are discussed. In numerical simulation, the one-link manipulator with revolute joints actuated by a DC motor is modeled to reflect the industrial application scenarios.

In this article, the quasi-synchronization for a kind of coupled neural networks with time-varying delays is investigated via a novel event-triggered impulsive control approach. In view of the randomly occurring uncertainties (ROUs) in the communication channels, the global quasi-synchronization for the coupled neural networks within a given error bound is considered instead of discussing the complete synchronization. A kind of distributed event-triggered impulsive controllers is presented with considering the Bernoulli stochastic variables based on ROUs, which works at each event-triggered impulsive instant. According to the matrix measure method and the Lyapunov stability theorem, several sufficient conditions for the realization of the quasi-synchronization are successfully derived. Combining with the mathematical methodology with the formula of variation of parameters and the comparison principle for the impulsive systems with time-varying delays, the convergence rate and the synchronization error bound are precisely estimated. Meanwhile, the Zeno behaviors could be eliminated in the coupled neural network with the proposed event-triggered function. Finally, a numerical example is presented to prove the results of theoretical analysis.

This article is devoted to studying the bipartite synchronization issue of multicoupled complex dynamic networks with mismatched parameters. A generalized processing analysis method for dealing with the network with derivative coupling is first presented. To acquire suitable input intervals, a novel memory-based self-triggered impulsive controller is elaborately designed. Accordingly, the triggering moments are precisely determined, which take the average error states of a small fraction of monitoring moments into account. Sufficient conditions for the bipartite synchronization are eventually obtained by utilizing the Lyapunov stability theorem in conjunction with the parameter variation approach and definition of average impulsive interval. Since time-varying impulsive effects are considered, the definition of average impulsive gain is introduced in order to estimate the convergence rates and error bounds, respectively. The capability of derived mathematical deductions is ultimately demonstrated by numerical examples. Further, comparative experiments are given to show the superiority of performance within three event-based mechanisms.

Synchronization of complex networks with nonlinear couplings and distributed time-varying delays is investigated in this article. Since the mismatched parameters of individual systems, a kind of leader-following quasisynchronization issues is analyzed via impulsive control. To acquire appropriate impulsive intervals, the dynamic self-triggered impulsive controller is devoted to predicting the available instants of impulsive inputs. The proposed controller ensures the control effects while reducing the control costs. In addition, the updating laws of the dynamic parameter is settled in consideration of error bounds to adapt to the quasisynchronization. With the utilization of the Lyapunov stability theorem, comparison method, and the definition of average impulsive interval, sufficient conditions for realizing the synchronization within a specific bound are derived. Moreover, with the definition of average impulsive gain, the parameter variation scheme is extended from the fixed impulsive effects case to the time-varying impulsive effects case. Finally, three numerical examples are given to show the effectiveness and the superiority of proposed mathematical deduction.

This article mainly studies the projective quasisynchronization for an array of nonlinear heterogeneous-coupled neural networks with mixed time-varying delays and a cluster-tree topology structure. For the sake of the mismatched parameters and the mutual influence among distinct clusters, the exponential and global quasisynchronization within a prescribed error bound instead of complete synchronization for the coupled neural networks with clustering trees is investigated. A kind of pinning impulsive controllers is designed, which will be imposed on the selected neural networks with some largest norms of error states at each impulsive instant in different clusters. By employing the concept of the average impulsive interval, the matrix measure method, and the Lyapunov stability theorem, sufficient conditions for the realization of the cluster projective quasisynchronization are derived. Meanwhile, in terms of the formula of variation of parameters and the comparison principle for the impulsive systems with mixed time-varying delays, the convergence rate and the synchronization error bound are precisely estimated. Furthermore, the synchronization error bound is efficiently optimized based on different functions of the impulsive effects. Finally, a numerical experiment is given to prove the results of theoretical analysis.

This article investigates adaptive control and exponential synchronization of a kind of derivative coupled complex dynamical networks (CDNs) with proportional delay. Based on impulsive control and adaptive pinning control protocols, sufficient criteria for achieving of the exponential synchronization on CDNs are obtained by jointly applying the proportional delayed impulsive comparison principle, the extended parameters variation formula and the definition of average impulsive interval. Meanwhile, suitable control gains for achieving adaptive synchronization are acquired according to the efficiently designed adaptive updating laws. In addition, the convergence velocity of the exponential synchronization is precisely estimated. Finally, one numerical simulation is presented to illustrate the validity of the adaptive pinning control protocols and theoretical results. By introducing the concept of impulsive distance for the first time, the example further explains the dynamic balance between the impulsive effects and the feedback control gains, which provides a method in controller designing.

This article is devoted to study the cluster synchronization for a kind of complex dynamical networks consisting of nonidentical nonlinear Lur'e systems. Different from general time delays, a proportional delay is taken into consideration in this article, which is a kind of unbounded time-varying delays and thus largely increases the difficulty in network synchronization. In consideration of the topology structures of the Lur'e networks, an effective impulsive pinning controller is proposed, which will be placed on the Lur'e systems having directed paths with those in the other clusters. Considering different functional roles that the impulsive effects play, sufficient criteria for the cluster synchronization of the nonidentically coupled Lur'e dynamical networks are obtained by applying the proportionally delayed impulsive comparison principle, the concept of average impulsive interval, and the extended parameters variation formula. Simultaneously, the exponential convergence rates are successfully estimated with respect to different functions of the impulsive effects. In the end of this article, three numerical simulations are proposed to denote the effectiveness of the control protocols and the theoretical results.

This paper investigates the exponential synchronization of coupled Lur'e dynamical networks with multiple time-varying delays and derivative coupling. In order to synchronize the Lur'e dynamical networks to the corresponding Lur'e systems, we propose a kind of impulsive pinning control strategy, where different functions of impulsive effects are taken into account. Sufficient conditions are derived for the exponential synchronization of the derivative coupled Lur'e dynamical networks by jointly applying the contradiction proof method, the concept of an average impulsive interval, comparison principle, and the extended parameters variation formula. Simultaneously, the convergence rates of exponential synchronization are obtained according to the definition of the impulsive solution equation on different functions of impulsive effects. Furthermore, three numerical examples are presented to demonstrate the validity of the theoretical analysis and the control protocol.

This paper investigates the exponential synchronization of nonidentically coupled Lur'e dynamical networks with proportional delay. Since the heterogeneities existed in different Lur'e systems, quasi-synchronization rather than complete synchronization is thus discussed. Different from general time delay, the proportional delay is a type of unbounded time-varying delay, which tremendously increases the requirements on network synchronization. Based on distributed impulsive pinning control protocol and different roles that impulsive effects play, the criteria for quasi-synchronization of nonidentically coupled Lur'e dynamical networks are derived by jointly applying the delayed impulsive comparison principle, the extended formula for the variation of parameters, and the definition of an average impulsive interval. Moreover, synchronization errors for different impulsive effects with different functions are evaluated and simultaneously, the corresponding exponential convergence rates are obtained. In addition, three numerical examples are presented to illustrate the validity of the control scheme and the theoretical analysis.

This paper is concerned with the exponential synchronization issue of nonidentically coupled neural networks with time-varying delay. Due to the parameter mismatch phenomena existed in neural networks, the problem of quasi-synchronization is thus discussed by applying some impulsive control strategies. Based on the definition of average impulsive interval and the extended comparison principle for impulsive systems, some criteria for achieving the quasi-synchronization of neural networks are derived. More extensive ranges of impulsive effects are discussed so that impulse could either play an effective role or play an adverse role in the final network synchronization. In addition, according to the extended formula for the variation of parameters with time-varying delay, precisely exponential convergence rates and quasi-synchronization errors are obtained, respectively, in view of different types impulsive effects. Finally, some numerical simulations with different types of impulsive effects are presented to illustrate the effectiveness of theoretical analysis.

This paper is devoted to the finite-time cluster synchronization issue of nonlinearly coupled complex networks which consist of discontinuous Lur'e systems. On the basis of the definition of Filippov regularization process and the measurable selection theorem, the discontinuously nonlinear function is mapped into a function-valued set, then a measurable function is accordingly selected from the Filippov set to ensure the existence of the solution for the discontinuous system. By designing the finite-time pinning controller, some sufficient conditions are obtained for cluster synchronization of the identical and nonidentical Lur'e networks, respectively. In addition, the settling time for achieving the cluster synchronization is estimated by applying the finite-time stability theory. And finally, a numerical example is presented to illustrate the validity of theoretical analysis.