Synchronization Analysis for Complex Dynamical Networks With Coupling Delay via Event-Triggered Delayed Impulsive Control

Secure synchronization control for complex dynamic networks with event-triggered communication strategy under multi-channel denial-of-service attacks

This article addresses the secure synchronization problem for complex dynamical networks (CDNs) with observer-based event-triggered communication strategy (ETCS) under multi-channel denial-of-service attacks (MCDSAs). Due to external environmental interference, the observers are designed to accurately estimate the state of the network systems. Meanwhile, the impact of cyber attacks on system security is considered. Differing from other studies, MCDSAs in this paper are considered, which present the interference of malicious attacks on the communication topology, observers and controllers. Based on the characteristics of cyber attacks, the model for CDNs with nonperiodic switching topology is established, and the observer-based intermittent control is proposed to achieve synchronization of CDNs. To decrease the network communication frequency and reduce the risk of cyber attacks, a new ETCS depending on estimate states is designed. Then, using Lyapunov stability theory, several synchronization conditions depending on the status parameters of MCDSAs are deduced, which may estimate the allowable ranges for the duration and frequency of MCDSAs. From these theoretical results, it can be observed that the destructive power of network attacks increases exponentially with the increase of attack duration. Finally, from simulation experiments, the availability of the designed controller and communication strategy is verified, which can ensure the synchronization for CDNs with MCDSAs.

Synchronization of complex dynamical networks with saturated delayed impulsive control

This paper considers the local exponential synchronization problem for a type of complex dynamical networks (CDNs) with both system delay and coupled delay using saturated delayed impulsive control. Based on the methods of average impulsive interval (AII), average impulsive delay (AID) and average impulsive estimation (AIE), a Razumikhin-type inequality with hybrid delayed impulses (which include delayed impulses and delay-free impulses) is derived. This inequality includes pure delayed impulsive inequalities. By utilizing the constructed inequality and the Lyapunov stability theory, the saturation nonlinearities are treated as the convex hulls, and sufficient synchronization criteria for local exponential synchronization of CDNs are presented in the framework of linear matrix inequalities (LMIs). Moreover, to enlarge the estimation of region of attraction (ROA) and the design of impulsive control gain, a convex optimization problem based on LMIs is formulated. Finally, a numerical example demonstrates the effectiveness of the obtained results.

DoS attacks resilience of heterogeneous complex networks via dynamic event-triggered impulsive scheme for secure quasi-synchronization

This paper addresses the secure quasi-synchronization issue of heterogeneous complex networks (HCNs) under aperiodic denial-of-service (DoS) attacks with dynamic event-triggered impulsive scheme (ETIS). The heterogeneity of networks and the aperiodic DoS attacks, which hinder communication channels and synchronization goals, present challenges to the analysis of secure quasi-synchronization. The ETIS leverages impulsive control and dynamic event-triggered scheme (ETS) to handle the network heterogeneity and the DoS attacks. We give specific bounds on the attack duration and frequency that the network can endure, and obtain synchronization criteria that relate to event parameters, attack duration, attack frequency, and impulsive gain by the variation of parameter formula and recursive methods. Moreover, we prove that the dynamic ETS significantly reduces the controller updates, saves energy without sacrificing the system decay rate, and prevents the Zeno phenomenon. Finally, we validate our control scheme with a numerical example.

Event-triggered protocol-based adaptive impulsive control for delayed chaotic neural networks

This article focuses on the synchronization problem of delayed chaotic neural networks via adaptive impulsive control. An adaptive impulsive gain law in a discrete-time framework is designed. The delay is handled skillfully by using the Lyapunov-Razumikhin method. To improve the flexibility of impulsive control, an event-triggered impulsive strategy to determine when the impulsive instant happens is designed. Additionally, it is proved that the event-triggered impulsive sequence cannot result in the occurrence of Zeno behavior. Some criteria are derived to guarantee synchronization for delayed chaotic neural networks. Eventually, an illustrative example is presented to empirically validate the effectiveness of the suggested strategy.

Event-triggered hybrid impulsive control for synchronization of fractional-order multilayer signed networks under cyber attacks

In this paper, we consider the exponential bipartite synchronization (EBS) problem of fractional-order multilayer signed networks with time-varying delays (FO-MSNT) under random cyber attacks. In contrast to the existing literature, the proposed hybrid event-triggered controller combines the advantages of feedback controller and impulsive controller, and the event-triggered condition is constructed by applying the network topology and the Lyapunov function of the subsystem, rather than the state function of the subsystem. Based on the Lyapunov-Razumikhin method and the graph theory, some sufficient conditions for achieving EBS of FO-MSNT under cyber attacks which are related to the topology of networks, the event-triggered parameters, the order of fractional derivative and the signal sent by the enemy are obtained. Furthermore, fractional-order coupled Chua's circuits model and fractional-order power systems built on MSNT are established and the EBS issues under cyber attacks are analyzed. Numerical examples and simulations are provided to show the validity of our theories.

Global μ-synchronization for coupling delayed complex dynamical networks via event-triggered delayed impulsive control

This paper mainly focuses on solving the global μ-synchronization issue of complex dynamical networks (CDNs) by a novel event-triggered impulsive control (ETIC) method with time delays. This method combines the advantages of impulsive control and event-triggered control and gets rid of the limitation that the Lyapunov function decreases strictly monotonically with the sequence of event triggers. An event-triggered mechanism is specifically designed to realize μ-synchronization for CDNs in this paper, which means that event-triggered control has been applied to μ-synchronization field for the first time. Compared with periodic impulsive control, ETIC only produces control effects when the event-triggered mechanism are met, which is more in line with the actual situation. By Lyapunov-Razumikhin, recursion, etc, some valid global μ-synchronization criteria of CDNs are obtained and also Zeno behavior is avoided. Additionally, coupled delays and uncertainties are considered in CDNs. Finally, two numerical examples are shown to demonstrate the correctness of the designed ETIC strategy.

Local Synchronization of Directed Lur'e Networks With Coupling Delay via Distributed Impulsive Control Subject to Actuator Saturation

This article studies the local exponential synchronization synthesis problem of directed Lur'e networks with coupling time-varying delay under the distributed impulsive control subject to actuator saturation. First, by utilizing proof by contradiction, impulsive comparison principle, and latest improved convex hull representation of saturation function, some delay-independent sufficient criteria for local exponential synchronization are presented in the form of bilinear matrix inequalities. Meanwhile, a novel method with less conservatism is developed to estimate the domain of attraction, which is radically different from the traditional method by means of contractive invariant set. Second, optimization problems constrained by the transformed linear matrix inequalities are established to acquire the maximum estimates of both the domain of attraction and average impulsive interval (AII), which are conveniently solved by the YALMIP toolbox in MATLAB software. Finally, a numerical simulation is rendered to demonstrate the effectiveness and advantages of the proposed theoretical results.

Synchronization of hybrid switching diffusions delayed networks via stochastic event-triggered control

In this paper, the synchronization problem of stochastic complex networks with time delays and hybrid switching diffusions (SCNTH) is concerned based on event-triggered control. Therein, a new class of event-triggered function is proposed for the control design. Particularly, different from the existing work, the triggered instant generated by event-triggered control in this paper is a stochastic sequence instead of a number sequence to be more realistic for stochastic systems, which is a breakthrough. Furthermore, some sufficient conditions are derived to guarantee asymptotical synchronization in mean square, exponential synchronization in mean square and almost surely exponential synchronization of SCNTH based on sampled-data control, event-driven control theory and stability analysis. Meanwhile, the Zeno phenomenon can be avoided. Then, the synchronization of single-link robot arms is investigated in detail as a practical application of the obtained results. Ultimately, a numerical example is given for demonstration.

Cluster synchronization of delayed coupled neural networks: Delay-dependent distributed impulsive control

This paper investigates the issue of cluster synchronization (CS) for the coupled neural networks (CNNs) with time-varying delays via the delay-dependent distributed impulsive control. A new Halanay-like inequality, where delayed impulses are taken into consideration, is proposed. Based on the Lyapunov theory and the new differential inequality, sufficient conditions of CS for delayed CNNs with fixed and switching coupling topology are obtained, respectively. Moreover, delay-dependent distributed impulsive controllers with fixed or switching topology are designed thereby. Finally, we present a numerical example of CNNs with fixed or switching coupling to verify the effectiveness of our results, respectively.

A Novel Strategy for Complete and Phase Robust Synchronizations of Chaotic Nonlinear Systems

Our work here is to propose a novel technique by which chaos complete and phase synchronizations can be accomplished via a low-cost scheme. We call the proposed technique a “single-state feedback track synchronization control algorithm”. A single-state feedback track synchronization control algorithm is designed so that both complete and phase synchronizations can be accomplished using the same controller. Complete synchronization between two chaotic systems means complete symmetry between them, but phase synchronization means complete symmetry with a phase shift. In addition, the proposed method is applied to the synchronization of two identical chaotic Lorenz models. The effectiveness and robustness of the proposed algorithm is well illustrated via exhaustive numerical simulation experiments based on the Matlab toolbox of the powerful genetic algorithm. The robustness of the proposed algorithm motivated us to apply this method of synchronization in a secure communication application.