Synchronization Criteria Research Articles

Sampled-Data-Based Event-Triggered Synchronization Strategy for Fractional and Impulsive Complex Networks With Switching Topologies and Time-Varying Delay

In this article, the sampled-data-based event-triggered synchronization control for fractional and impulsive complex networks (CNs) with time-varying delay is investigated and a class of more general network structure based on the switching topologies at impulsive instants is considered. First, a class of novel fractional-order integral inequalities is produced to obtain depend-delay synchronization criteria and estimate Lyapunov–Krasovskii functions. Then, a sampled-data-based event-triggered control is designed, which can ensure synchronization of fractional and impulsive CNs (FICNs) with time-varying delay. Next, by using the Lyapunov direct method, some criteria are obtained to guarantee the synchronization of FICNs. Numerical simulations are given to demonstrate that the designed sampled-data-based event-triggered synchronization strategy can effectively not only achieve synchronization of FICNs but reduce the frequency of controller update compared to the previous related works.

Finite-Time Projective Synchronization and Parameter Identification of Fractional-Order Complex Networks with Unknown External Disturbances

This paper is devoted to exploring the finite-time projective synchronization (FTPS) of fractional-order complex dynamical networks (FOCDNs) with unknown parameters and external disturbances. Based on the stability theory of fractional-order differential systems, synchronization criteria between drive-response networks were obtained and both the uncertain parameters and external disturbances were identified or conquered simultaneously. Moreover, the upper limit of the settling-time function was obtained. Finally, a numerical example was given to verify the effectiveness of the results.

Impulsive Synchronization of linear complex dynamical networks with time delay on time scales

In this paper, we investigate the impulsive synchronization of linear complex dynamical networks(CDNs) with time delay on time scales by a method of pinning impulsive control. We use the time scales theory and the Lyapunov method to derive a synchronization criterion. We find that we can achieve the synchronization of CDNs through only controlling a small number of nodes and the modeling framework here can enrich the models of continous/discrete-time CDNs. In the end, we give some numerical simulations to demonstrate the feasibility of the theoretical analysis.

Bipartite leader-following synchronization of fractional-order delayed multilayer signed networks by adaptive and impulsive controllers

This article addresses the problem of bipartite leader-following synchronization of fractional-order delayed multilayer signed networks. It is worth emphasizing that fractional dynamics and multiple connections between nodes with multiple time delays are considered into signed networks. In our main results, adaptive control (continuous control) and impulsive control (discontinuous control) are both designed to reach the bipartite leader-following synchronization of the underlying networks. In addition, a Halanay inequality of fractional version is established. With the help of it, by using signed graph theory and Lyapunov method, some bipartite synchronization criteria are derived under the Lyapunov-type theorems and coefficients-type theorems. Then, as an application of theoretical results, the bipartite leader-following synchronization of fractional-order coupled Chua’s circuits modeled on delayed multilayer signed networks is considered. Finally, two numerical examples are exhibited to exemplify the usefulness and feasibility of the theoretical results.

Lag quasi-synchronization of incommensurate fractional-order memristor-based neural networks with nonidentical characteristics via quantized control: A vector fractional Halanay inequality approach

This work realizes lag quasi-synchronization of incommensurate fractional-order memristor-based neural networks (FMNNs) with nonidentical characteristics via quantized control. The motivations behind this research work are threefold: (1) quantized controllers, which generate discrete control signals, can be more easily realized in computers than non-quantized controllers, and can consume smaller communication capacity; (2) incommensurate orders in a single FMNN and nonidentical characteristics in drive-response FMNNs are inescapable due to the differences among the circuit elements used to implement FMNNs; (3) convergence analysis of delayed incommensurate fractional-order nonlinear systems, which is the basis for the derivation of synchronization criterion, has not been handled perfectly. As an effective tool for convergence analysis of delayed incommensurate fractional-order nonlinear systems, especially for estimation of ultimate state bound, a vector fractional Halanay inequality is established at first. Then, a quantized synchronization controller, in which the dead-zone is introduced into some logarithmic quantizers to avoid chattering phenomenon, is designed. By means of vector Lyapunov function together with the newly derived vector fractional Halanay inequality, the synchronization criterion is proved theoretically. Lastly, numerical simulations supplementarily illustrate the correctness of the synchronization criterion. In contrast with the hypotheses in the relevant literature, the hypotheses in this paper are weaker.

Quasi-Synchronization and Quasi-Uniform Synchronization of Caputo Fractional Variable-Parameter Neural Networks with Probabilistic Time-Varying Delays

Owing to the symmetry between drive–response systems, the discussions of synchronization performance are greatly significant while exploring the dynamics of neural network systems. This paper investigates the quasi-synchronization (QS) and quasi-uniform synchronization (QUS) issues between the drive–response systems on fractional-order variable-parameter neural networks (VPNNs) including probabilistic time-varying delays. The effects of system parameters, probability distributions and the order on QS and QUS are considered. By applying the Lyapunov–Krasovskii functional approach, Hölder’s inequality and Jensen’s inequality, the synchronization criteria of fractional-order VPNNs under controller designs with constant gain coefficients and time-varying gain coefficients are derived. The obtained criteria are related to the probability distributions and the order of the Caputo derivative, which can greatly avoid the situation in which the upper bound of an interval with time delay is too large yet the probability of occurrence is very small, and information such as the size of time delay and probability of occurrence is fully considered. Finally, two examples are presented to further confirm the effectiveness of the algebraic criteria under different probability distributions.

Particle swarm optimization algorithm for dynamic synchronization of smart grid

ABSTRACT In recent decades, traditional energy generation and consumption have undergone a transformation to cleaner energy sources. The transition to a sustainable energy system based on efficiency and renewable energies will thus require the replacement of a complex and heavily implemented energy system with one based on concepts such as microgrids. A microgrid is a controlled small-scale power system and the elements that make up it are: distributed generation systems; energy storage systems; load management techniques; monitoring systems, etc. Consequently, since ac devices are used, synchronization criteria must be satisfied to switch operation between them. The synchronization criteria consist of making the values of the phase-angle difference, slip frequency, and voltage difference as small as possible. This is very important to ensure the correct operation of the grid. In the other hand, the use of Particle Swarm Optimization (PSO) algorithm has been increasing, because of their simplicity and efficiency in engineering optimization problems. Therefore, this paper proposes an active synchronizing control scheme that allows to synchronize a generator set to the grid and a particle swarm optimization algorithm, which makes the synchronizing control as efficient as possible. With the implemented control and with the help of the synchronization algorithm, improvements in the reduction of settling time (from 9 seconds to 3 seconds) are obtained in comparison to other controls in the literature.

An asymptotic state estimator design and synchronization criteria for fractional order time‐delayed genetic regulatory networks

AbstractThis paper mainly investigates the asymptotic state estimator design and impulsive controlled synchronization for fractional‐order time‐delayed genetic regulatory networks (FOTDGRNs). Different from the existing state estimator results, the asymptotic state estimator design of FOTDGRNs is studied by using a novel algebraic method, fractional‐order Lyapunov–Razumikhin method, and some famous inequality techniques. Afterward, a suitable impulsive controller is designed for the global asymptotic synchronization criteria for addressing master–slave systems. At last, the paper comes up with two numerical cases to justify the applicability of our theoretical outcomes.

Fixed-Time Synchronization for Fuzzy-Based Impulsive Complex Networks

This paper mainly deals with the issue of fixed-time synchronization of fuzzy-based impulsive complex networks. By developing fixed-time stability of impulsive systems and proposing a T-S fuzzy control strategy with pure power-law form, some simple criteria are acquired to achieve fixed-time synchronization of fuzzy-based impulsive complex networks and the estimation of the synchronized time is given. Ultimately, the presented control scheme and synchronization criteria are verified by numerical simulation.

PID Control for Output Synchronization of Multiple Output Coupled Complex Networks

This article attempts to address output synchronization and <inline-formula><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> output synchronization problems for multiple output coupled complex networks (MOCCNs) under proportional-derivative (PD) and proportional-integral (PI) controllers. Firstly, two classes of MOCCNs without and with external disturbances are separately put forward. Secondly, based on the PD and PI control schemes, several output synchronization criteria for MOCCNs are formulated by using the Lyapunov functional method and inequality techniques. Thirdly, <inline-formula><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> output synchronization for MOCCNs is also studied with the help of the PD and PI controllers. Finally, two numerical examples are separately presented to demonstrate the validity of acquired theoretical results.

Global [formula omitted]-synchronization for nonlinear complex networks with unbounded multiple time delays and uncertainties via impulsive control

The global μ-synchronization problem of nonlinear drive–response complex networks with uncertainties is investigated in this paper. Unbounded multiple time delays, such as internal delays, coupling delays, and sampling delays in impulse instants are considered in our complex network model. The difficulties caused by these multiple time delays are overcome by introducing a generalized impulsive delayed comparison principle. A delayed impulsive controller is designed, and some novel synchronization criteria are derived in order to make drive–response complex networks achieve μ-synchronization. Compared with the existing related works, there is no restriction about impulse intervals and delays, as well as, the external coupling matrix is no longer needed to satisfy the dissipative coupling condition. Finally, two numerical simulations are shown to present the correctness of our theoretical results.

Dynamic analysis of delayed neural networks: Event-triggered impulsive Halanay inequality approach

This paper proposes a generalized impulsive Halanay inequality from the impulsive control standpoints, where the impulse action is event-triggered. Namely, the control task is executed when an external event generated by the state-dependent event-triggered mechanism (ETM) is activated, rather than at a fixed time. It is shown that under the proposed event-triggered impulsive control (ETIC) strategy, the solution of the underlying inequality is guaranteed to converge to zero asymptotically. Moreover, the key point is the introduction of monitoring value to ensure a positive minimum inter-execution time, which exactly assists ETIC with reducing the pressure of information transmission. Then, the generalized impulsive Halanay inequality with appropriate ETIC scheme is utilized to the analysis of delayed neural networks (DNNs). In particular, some synchronization and asymptotic stability criteria of DNNs are derived, where the design of impulsive controller is based on ETIC strategy. At last, some numerical examples are provided to illustrate the validity of the obtained results.

Synchronization behaviors of a vibrating mechanical system with adjustable frequencies and motion trajectories

In present work, the double and triple-frequency synchronization behaviors of a vibrating mechanical system with two different driving frequencies, driven by three reversed rotating exciters, are investigated by theory, numeric, and experiment. Based on Lagrange’s equations, the dynamic model corresponding to vibrating machine is proposed and motion differential equations are constructed. The Bogoliubov standard formal equations for three exciters are established, by introducing the asymptotic method, in which the synchronization problem is converted into that of the existence and stability of zero-valued solution of the average differential equations. The synchronization criterion of satisfying the synchronous operation is deduced. According to the Routh–Hurwitz criterion, the stability criterion of the synchronous states is achieved analytically. Based on the obtained theory results, the stability characteristics of the system, are numerically discussed in detail, including the stability ability coefficients and stable phase differences. Finally, simulations and experiments under the condition of two different driving frequencies, are performed to further examine the validity of the theoretical and numerical qualitative results. The present work can provide a theoretical reference for designing some new types of the vibrating machines with adjustable frequencies and motion trajectories.

Synchronization of complex networks with hybrid delays based on event intermittent control

This paper studies the exponential synchronization problem for complex networks with hybrid delays via means of the event intermittent control (EIC) strategy. Compared with the traditional aperiodically intermittent control, the control instants and the rest instants are generated when the events occur, which is more in accordance with the actual situation. An modified lemma related to delays is derived without predesigning intermittent instants. Furthermore, some synchronization criteria with less conservatism are established in terms of linear matrix inequalities (LMIs). Meanwhile, it is also shown that Zeno behavior is excluded. Finally, simulations of a numerical example are given to verify the effectiveness of the proposed EIC strategy.

Event‐triggered H∞$\mathcal {H}_\infty$ synchronization of directed and switched coupled stochastic delayed neural networks with multi‐weights

This essay is devoted to studying H ∞ $\mathcal {H}_\infty$ synchronization problem of directed and switched coupled stochastic delayed neural networks with multi-weights (SCSDNNMWs) via designing a novel event-triggered protocol. The proposed model is based on stochastic delayed neural network with directed coupling, and multiple coupling matrices with switching express intricate and changing communication channels. Since the external disturbances are likely to cause network topologies change, fixed and accurate values of coupling matrices are difficult to obtain, while the above model has more advantages of characterizing this real network. Besides, zero eigenvalue of different coupling matrices are represented by the corresponding normalized left eigenvectors (NLEVec), which is hard to establish yet especially when designing necessary Lyapunov functions. The authors' essay deduces that if the Chebyshev distance among NLEVec of multiple coupling matrices is less than a permissible deviation limit based on a weighted set of these NLEVec, then several event-triggered H ∞ $\mathcal {H}_\infty$ synchronization and synchronization criteria are established. The effectiveness of these results are verified by several given examples.

Synchronization implementation of two eccentric rotors actuated with swung and fixed motors

In a vibrating screen machinery, two eccentric rotors (ERs) are actuated by swung and fixed motors. When the working efficiency of vibrating screens is the highest, the motion trajectory of the vibrating body is an ellipse. However, to implement elliptical trajectory, the ideal synchronization between the two ERs must be needed. Hence, the self-synchronous theory and synchronous control method for the vibrating screen machinery are explored. First, the mathematic model of the vibration system is deduced based on Lagrange equation; then, the synchronous condition and stability criterion are inferred from averaged small parameter method. In addition, the synchronization controllers, related to speed and phase of the ERs, are designed by with sliding mode control (SMC), and the master–slave control strategy is applied to design the control structure. Meanwhile, the stability performance of the controllers is demonstrated by Lyapunov theory and Hurwitz condition. Finally, computer simulations are implemented to validate the theoretical reliability of self-synchronization and synchronous control. The simulation results show that the system can be self-synchronized, but the ideal synchronization is difficult to achieve when the two ERs are self-synchronously rotated, which leads to non-ideal dynamic characteristics; nevertheless, the ideal synchronization can be implemented by the proposed synchronous control method.

Finite-time generalized synchronization of non-identical fractional order chaotic systems and its application in speech secure communication.

This paper focuses on the finite-time generalized synchronization problem of non-identical fractional order chaotic (or hyper-chaotic) systems by a designing adaptive sliding mode controller and its application to secure communication. The effects of both disturbances and model uncertainties are taken into account. A novel fractional order integral sliding mode surface is designed and its stability to the origin is proved in a given finite time. By the aid of the fractional Lyapunov stability theory, a robust controller with adaptive update laws is proposed and its finite-time stability for generalized synchronization between two non-identical fractional-order chaotic systems in the presence of model uncertainties and external disturbances is derived. Numerical simulations are provided to demonstrate the effectiveness and robustness of the presented approach. All simulation results obtained are in good agreement with the theoretical analysis. According to the proposed generalized finite-time synchronization criterion, a novel speech cryptosystem is proposed to send or share voice messages privately via secure channel. Security and performance analyses are given to show the practical effect of the proposed theories.

Fuzzy sampled‐data exponential synchronization of T‐S fuzzy complex networks with discontinuous activations and mixed time‐varying delays

This paper investigates the exponential synchronization for T-S fuzzy complex networks (TSFCNs) with discontinuous activations and mixed time-varying delays. Based on the IF-THEN rules, the T-S fuzzy model of complex networks has been obtained to approximate non-linear dynamic systems via interpolating certain local linear system. A fuzzy sampled-data control strategy is designed to achieve exponential stability for the TSFCN by constructing the bilateral time-dependent Lyapunov–Krasovskii functional. Furthermore, according to the Filippov discontinuity theory, the exponential synchronization criteria of TSFCN with discontinuous activations and mixed time-varying delays under the linear matrix inequality constraints are obtained. Finally, two numerical simulations are provided to illustrate the effectiveness and feasibility of the proposed method.

Synchronization and state estimation for discrete-time coupled delayed complex-valued neural networks with random system parameters

In this paper, an array of discrete-time coupled complex-valued neural networks (CVNNs) with random system parameters and time-varying delays are introduced. The stochastic fluctuations of system parameters, which are characterized by a set of random variables, are considered in the individual CVNNs. Firstly, the synchronization issue is solved for the considered coupled CVNNs. By the use of the Lyapunov stability theory and the Kronecker product, a synchronization criterion is proposed to guarantee that the coupled CVNNs are asymptotically synchronized in the mean square. Subsequently, the state estimation issue is studied for the identical coupled CVNNs via available measurement output. By establishing a suitable Lyapunov functional, sufficient conditions are derived under which the mean square asymptotic stability of the estimation error system is ensured and the design scheme of desired state estimator is explicitly provided. Finally, two numerical simulation examples are shown for the purpose of illustrating the effectiveness of the proposed theory.

Alternate periodic event-triggered control for synchronization of multilayer neural networks

In this paper, the exponential synchronization of multilayer neural networks (MNNs) is investigated via alternate periodic event-triggered control (APETC). Distinguished from the previous work, a novel APETC which incorporates aperiodically intermittent control (AIC) and periodic event-triggered mechanism is firstly proposed. Determined by two event-triggered conditions, the control and rest intervals of APETC are based on the present state of the system rather than being predetermined. In contrast to the conventional event-triggered control (ETC), the event-triggered conditions of APETC can not only judge the updates of control signals, but also dominate the actuation and close of the controller. Moreover, by introducing the sampling period into ETC, the number of event triggers can be decreased and the Zeno phenomenon is completely avoided. Subsequently, synchronization criteria for MNNs under APETC are established on the basis of Lyapunov method and graph theory. Finally, several numerical simulations are performed to demonstrate the validity of the theoretical results.