Synchronization Of Complex Dynamical Networks Research Articles

Cluster synchronization of complex dynamic networks under pinning control via a limited capacity communication channel

In this paper, the cluster synchronization pinning control problem is investigated for the continuous-time-directed complex dynamic networks under the bit rate constraint. Firstly, a node selection scheme based on differences in node degrees is proposed to achieve cluster synchronization. Subsequently, a coding–decoding scheme is designed during data transmission through digital communication channels where only a limited number of encoded signal sequences are sent to the controller side. Further, regarding the unreliability of the channel, the phenomenon of packet dropouts is considered during the encoding process, which is modeled by using a series of independent Bernoulli distributed random variables. The pinning controller is then designed based on the received decoding information. By means of the convex optimization method, a sufficient condition is established to ensure that the cluster synchronization error is ultimately bounded and the desired controller gain is determined based on the solution to matrix inequalities. Finally, the effectiveness of the obtained results is validated through a simulation example.

Adaptive Synchronization of Complex Dynamical Networks: Dealing With Uncertain Impulses

Adaptive Synchronization of Complex Dynamical Networks: Dealing With Uncertain Impulses

Adaptive memory event-triggered observer-based pinning synchronization control for complex dynamical networks under asynchronous attacks

This article addresses the security synchronization issue of complex dynamical networks under asynchronous cyber and physical attacks within the context of cyber-physical systems. An observer is devised to estimate the system's state using the measured outputs of partial nodes. The integration of a buffer for storing historical information enhances the accuracy of state estimation under asynchronous attacks, enabling the observer-based control scheme to generate more precise control signals during attacks. The robustness against external disturbances is reinforced by introducing disturbance compensation for both the observer and the controller. Additionally, an adaptive memory event-triggered mechanism is designed to conserve network resources. Then, a sufficient condition for the synchronization of complex dynamical networks against asynchronous attacks is obtained, and the gains of the observer and controller are computed based on the linear matrix inequality technique. Finally, a simulated example demonstrates the effectiveness of the suggested strategy.

Exponential Synchronization of Complex Dynamic Networks with Time Delay and Uncertainty via Adaptive Event-Triggered Control

In this paper, exponential synchronization problem of uncertain complex dynamic networks with time delay is studied via adaptive event-triggered control. Considering the influence of external environment, a new dynamic event-triggered mechanism is proposed, in order to reduce the transmission signal among nodes and reduce the consumption of communication resources. Moreover, in the proposed control mechanism, the controller is adaptive, that is, it only works when the triggering conditions are satisfied. Then, according to the designed adaptive event-triggered control strategy, the sufficient conditions for exponential synchronization are obtained by using Lyapunov functions and inequality technique. In addition, it is proved that the system can avoid Zeno behavior. At last, using two examples to verify the feasibility of the results.

Robustness Analysis of Exponential Synchronization in Complex Dynamic Networks with Deviating Argumentsand Parameter Uncertainties

In the paper, we study the robust synchronization of complex dynamic networks (CDNs) with deviating arguments and parameter uncertainties via self-feedback control, the model involves both advanced and delayed arguments. In addition, based on the Gronwall inequality and inequality techniques, we derive upper bounds on the length of the arguments and the magnitude of the parameters, when the parameters and arguments of CDNs are below the upper bounds, the CDNs continue to exhibit exponential synchronization. In comparison to linear matrix inequalities and Lyapunov’s method in the existing literature, we obtain elaborate bounds. Finally, Several simple examples can demonstrate the effectiveness of the results.

Local Synchronization for Delayed Complex Dynamical Networks via Self-Triggered Impulsive Control Involving Delays.

This article investigates the local synchronization for delayed complex dynamical networks (CDNs) under self-triggered impulsive control (STIC) approaches involving delays. With the help of Lyapunov-Razumikhin methods and comparison principle, some design criteria of STIC strategies ensuring local synchronization for delayed CDNs with delayed impulses are provided, and Zeno behavior can be avoided. Compared with the existing results on synchronization of CDNs under STIC, in this article, time delays in both continuous and discrete system dynamics are well considered. Moreover, the proposed self-triggered mechanism (STM) is an explicit expression, under which the next triggering instant can be derived directly, with simple structure and easy implementation. Finally, two numerical examples are provided to validate the proposed theoretical criteria.

Fuzzy adaptive event-triggered synchronization of complex dynamical networks via switched pinning control

Fuzzy adaptive event-triggered synchronization of complex dynamical networks via switched pinning control

Synchronization of Complex Dynamical Networks with Stochastic Links Dynamics.

The mean square synchronization problem of the complex dynamical network (CDN) with the stochastic link dynamics is investigated. In contrast to previous literature, the CDN considered in this paper can be viewed as consisting of two subsystems coupled to each other. One subsystem consists of all nodes, referred to as the nodes subsystem, and the other consists of all links, referred to as the network topology subsystem, where the weighted values can quantitatively reflect changes in the network's topology. Based on the above understanding of CDN, two vector stochastic differential equations with Brownian motion are used to model the dynamic behaviors of nodes and links, respectively. The control strategy incorporates not only the controller in the nodes but also the coupling term in the links, through which the CDN is synchronized in the mean-square sense. Meanwhile, the dynamic stochastic signal is proposed in this paper, which is regarded as the auxiliary reference tracking target of links, such that the links can track the reference target asymptotically when synchronization occurs in nodes. This implies that the eventual topological structure of CDN is stochastic. Finally, a comparison simulation example confirms the superiority of the control strategy in this paper.

Mean-square asymptotic synchronization of complex dynamical networks subject to communication delay and switching topology

Abstract This paper addresses the issue of mean-square asymptotic synchronization (MSAS) of complex dynamical networks with communication delay and switching topology. The communication delay is assumed to be time-variant and bounded, and the switching topology is governed by a semi-Markovian process and allowed to be asymmetric. A distributed control law based on state feedback is presented. Two criteria for the MSAS are derived using a mode-dependent Lyapunov-Krasovskii functional, the Bessel-Legendre integral inequality, and a parameter-dependent convex combination inequality, for the asymmetric and symmetric topology cases, respectively. The scenario of fixed topology is also considered, for which two asymptotic synchronization criteria are proposed. Two simulation examples are provided to illustrate the effectiveness and reduced conservatism of the proposed theoretical results.

Nonfragile Memory Sampled-Data Control for Exponential Synchronization of Complex Dynamical Networks With Time-Varying Coupling Delay

This article addresses the issue of exponential synchronization in complex dynamical networks. First, the nonfragile memory sampled-data control is used to mitigate the impact of controller uncertainties. Second, an augmented Lyapunov–Krasovskii functional (LKF) is built using a modified two-sided looped-functional that requires the positive definite only at sampling instants instead of throughout the sampling period. Moreover, the constructed LKF takes into account the whole sampling period and encompasses information on both the current states and the delayed states. Some exponential synchronization criteria are obtained by combining the Wirtinger-based integral inequality with the optimal reciprocally convex technology, and this scheme results in a larger sampling upper bound. At last, two extensively used numerical simulation examples confirm the proposed method's validity and advantage.

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.

Synchronization of complex dynamical networks subjected to actuator faults and periodic scaling attacks using probabilistic time-varying delays

In this paper, the synchronization problem of complex dynamical networks (CDNs) subjected to actuator faults and periodic scaling attacks using probabilistic time-varying delays is investigated. In order to handle the fault effects in actuators of proposed complex networks, an actuator fault model is considered. The major objective of this paper is to construct a memory state feedback controller with time-varying actuator faults that are asymptotically synchronized in the mean square sense to defend against periodic scaling attacks. By establishing suitable Lyapunov-Krasovskii functionals and applying Wirtinger-based integral inequality, sufficient conditions are derived in terms of linear matrix inequalities (LMIs) for the proposed system. Moreover, a time-varying delay is supposed to depend on probabilistic distribution conditions. Thus, the resulting criteria that emerge are based on the amount of the delay as well as the probability that the delay will have values at certain intervals. At last, the efficiency of our proposed work is demonstrated by two numerical simulations.

Adaptive fixed-time output synchronization for complex dynamical networks with multi-weights

This paper addresses fixed-time output synchronization problems for two types of complex dynamical networks with multi-weights (CDNMWs) by using two types of adaptive control methods. Firstly, complex dynamical networks with multiple state and output couplings are respectively presented. Secondly, several fixed-time output synchronization criteria for these two networks are formulated based on Lyapunov functional and inequality techniques. Thirdly, by employing two types of adaptive control methods, fixed-time output synchronization issues of these two networks are dealt with. At last, the analytical results are verified by two numerical simulations.

Synchronization of complex dynamical networks with hybrid coupling

For a strongly connected network, the network may achieve synchronization by coupling of nodes. However, as the size of the network increases, it is difficult for one node with higher degree to couple with all its neighbors, especially when the dimension of the isolated node’s dynamics is more than one. In order to solve this problem, a novel hybrid coupling strategy is proposed to make a complex dynamical network achieve synchronization, where only one random dimension of each node is coupled with its all neighbors, and the other dimension of the node is coupled with only one node. Several numerical simulations verify the effectiveness of the proposed strategy.

Stochastic synchronization for semi-Markovian complex dynamic networks with partly unknown transition rates

This paper investigates the synchronization of complex dynamic networks with time-varying delay and general semi-Markovian jump. The general transition rates include completely unknown and uncertain but bounded as two special cases. First, by introducing auxiliary vectors with a few nonorthogonal polynomials, two free-matrix-based integral inequalities are developed, which encompass some existing ones as special cases. Second, an integral- based delay-product-type Lyapunov-Krasovskii functional is constructed, which fully considers the information of time delay. By utilizing a deley-dependent controller, two sufficient conditions are derived to realize the global stochastic mean-square synchronization by employing the established inequalities to evaluate the infinitesimal generator of the functional. This paper takes all possibilities into consideration and divides the general transition rates into five cases, which is never investigated before. Finally a numerical example is given to show the effectiveness and practicality of the presented method.

Synchronization of Complex Dynamical Networks Subject to DoS Attacks: An Improved Coding-Decoding Protocol.

This article investigates the synchronization of communication-constrained complex dynamic networks subject to malicious attacks. An observer-based controller is designed by virtue of the bounded encode sequence derived from an improved coding-decoding communication protocol. Moreover, taking the security of data transmission into consideration, the denial-of-service attacks with the frequency and duration characterized by the average dwell-time constraint are introduced into data communication, and their influence on the coder string is analyzed explicitly. Thereafter, by imposing reasonable restrictions on the transmission protocol and the occurrence of attacks, the boundedness of coding intervals can be obtained. Since the precision of data is generally limited, it may lead to the situation that the signal to be encoded overflows the coding interval such that it results in the unavailability of the developed coding scheme. To cope with this problem, a dynamic variable is introduced to the design of the protocol. Subsequently, based on the Lyapunov stability theory, sufficient conditions for ensuring the input-to-state stability of the synchronization error systems under the communication-constrained condition and malicious attacks are presented. The validity of the developed method is finally verified by a simulation example of chaotic networks.

Prescribed-Time Synchronization of Complex Dynamical Networks With and Without Time-Varying Delays

This paper is concerned with prescribed-time synchronization of complex dynamical networks (CDNs) with and without time-varying delays. By designing suitable controllers, the CDNs containing directed spanning trees are obtained. Subsequently, with the help of Lyapunov Stability Theory, two sufficient conditions are obtained to enssure that CDNs reach synchronization within a prescribed finite time. Unlike the most existing works that the settling time is decided by initial conditions or control parameters, the proposed one can preassign it arbitrarily as needed. Finally, two examples are given to confirm the validity and effectiveness of the theoretical results.

Proportional-integral control for synchronization of complex dynamical networks under dynamic event-triggered mechanism

In this paper, the exponential synchronization problem is investigated for a class of continuous-time complex dynamical networks (CDNs) with proportional-integral control strategy and dynamic event-triggered mechanism (DETM). To reduce communication overhead, a novel DETM is proposed to decide whether a certain control signal generated by proportional-integral controller should be transmitted or not. The dynamics of each network node is analyzed in conjunction with the proposed proportional-integral strategy under the DETM, and then a sufficient condition for achieving exponential synchronization of CDNs is provided. The validity of the DETM is further verified by the exclusion of the Zeno behavior. The gain matrices of the controller and the parameters of the DETM are jointly designed. The effectiveness of the proportional-integral control strategy under the DETM is demonstrated by a numerical example.

Improved Nonfragile Sampled-Data Event-Triggered Control for the Exponential Synchronization of Delayed Complex Dynamical Networks

The exponential synchronization of complex dynamical networks (CDNs) under improved nonfragile sampled-data event-triggered control (INFSDETC) is investigated in this study. A meaningful yet challenging issue is solved, namely, it can adjust the triggering mode and the triggering frequency to adapt to more situations in the event-triggered scheme in which it is able to adjust the triggering condition exponentially and linearly, and dynamically adjust the triggering according to the time and state. By using control theory and Lyapunov analysis theory, an improved event-triggered controller was constructed for more intelligent control and to ensure exponential synchronization for CDNs. Lastly, significant numerical simulation examples are developed to show the usefulness and the performance of the proposed methods.

Dissipative Synchronization of Semi-Markov Jump Complex Dynamical Networks via Adaptive Event-Triggered Sampling Control Scheme

This article investigates the dissipative synchronization of complex dynamical networks (CDNs) with semi-Markov switching topological structures. First, by introducing a semi-Markov process, the model we investigated is more practical and stands for an extension of the Markov jump CDNs that have been widely studied. Second, an adaptive event-triggered sampling controller is newly proposed for semi-Markov jump CDNs, unlike the periodic event-triggered control scheme, the adaptive event-triggered sampling control strategy can further reduce the controller’s update frequency by adaptively adjusting its threshold. Moreover, with the help of a novel two-sided looped-functional and some advanced inequality techniques, the conservatism of the obtained result is greatly reduced. A sufficient synchronization condition that ensures the stochastic stability of the error system is established. Finally, to show the validity and superiority of the proposed method, several examples including some comparisons and applications are given in the simulation part.