Synchronization Criteria Research Articles

Mixed-Delay-Dependent Augmented Functional for Synchronization of Uncertain Neutral-Type Neural Networks with Sampled-Data Control

In this paper, the synchronization problem of uncertain neutral-type neural networks (NTNNs) with sampled-data control is investigated. First, a mixed-delay-dependent augmented Lyapunov–Krasovskii functional (LKF) is proposed, which not only considers the interaction between transmission delay and communication delay, but also takes the interconnected relationship between neutral delay and transmission delay into consideration. Then, a two-sided looped functional is also involved in the LKF, which effectively utilizes the information on the intervals [tk,t], [tk−τ,t−τ],[t,tk+1),[t−τ,tk+1−τ). Furthermore, based on the suitable LKF and a free-matrix-based integral inequality, two synchronization criteria via a sampled-data controller considering communication delay are derived in forms of linear matrix inequalities (LMIs). Finally, three numerical examples are carried out to confirm the validity of the proposed criteria.

Master–slave synchronization of fractional-order memristive MAM neural networks with parameter disturbances and mixed delays

In order to describe the system as realistically as possible, the fractional-order memristive multidirectional associative memory neural networks (FOMMAMNNs) with parameter disturbances, time-varying and distributed delays are established. Further, the master–slave synchronization is explored. Firstly, in the Filippov’s sense, some conditions are derived via the contraction mapping principle to guarantee the uniqueness of equilibrium point of the system. Secondly, from the perspective of reducing control costs, pinning controller and adaptive pinning controller are designed for the first time to induce synchronization of FOMMAMNNs. Moreover, some synchronization criteria are obtained by using the properties of fractional calculus, the appropriate Lyapunov candidate functions and fractional Barbalat’s lemma. Thirdly, a communication scheme based on chaotic synchronization is proposed to achieve the safe transmission of important information. Finally, two numerical simulations are given to illustrate the feasibility of the theoretical results and the security of the designed communication scheme.

Sliding-Mode Synchronization Control of Complex-Valued Inertial Neural Networks With Leakage Delay and Time-Varying Delays

This work explores the synchronization problem of two nonidentical complex-valued inertial neural networks (CVINNs) considering time-varying delays, leakage delay, and external disturbances. The entire analysis does not use reduced-order conversion, nor does it involve the separation of real and imaginary parts, but directly focuses on the original system. First, an integral sliding-mode surface suitable for the system is proposed. Second, the efficient sliding-mode control laws are designed, under which the state trajectories of the closed-loop dynamic error systems can be driven onto the predefined sliding-mode surface in finite time. Then, not requiring the time-varying delays to be differentiable, by constructing innovative Lyapunov–Krasovskii functionals, the synchronization criteria are obtained in the forms of the linear matrix inequality techniques. Eventually, for the systems with different types of activation functions, the corresponding numerical verification and comparison are carried out.

Dissipative Sliding-Mode Synchronization Control of Uncertain Complex-Valued Inertial Neural Networks: Non-Reduced-Order Strategy

This study investigates the dissipative synchronization of uncertain complex-valued inertial neural networks with external disturbances using sliding mode control (SMC). In the absence of both variable substitution as well as the equivalent transformations of real- and complex-valued systems, this study focuses directly on the original complex-valued inertial system. First, a suitable integral switching surface (SS) function is proposed. Second, by constructing innovative Lyapunov-Krasovskii functionals and applying the Wirtinger-based integral inequality and reciprocally convex approach, a synchronization criterion is derived on the basis of the linear matrix inequality technique to ensure that the sliding mode dynamics are stable and dissipative. Then, an SMC law and an adaptive SMC law are designed, and the accessibility analysis of the predefined SS is provided. Numerical verifications as well as the superiority and practicality analysis of the proposed approach are provided through four examples.

Synchronization of coupled map lattices

AbstractIn this paper, we address the issue of synchronization of coupled systems, introducing concepts of local and global synchronization for a class of systems that extend the model of coupled map lattices. A criterion for local synchronization is given; numerical experiments are exhibited to illustrate the criteria and also to raise some questions in the end of the text.

Secure Communication in Complex Dynamical Networks via Time-Delayed Feedback Control

In this article, a synchronization method of complex dynamical networks (CDNs) with time-varying delay feedback control is proposed to secure communication between the command system and each node of CDNs. To advance the security of the communication between the command system and each node of CDNs, the original information signal transmitted from the command system is encrypted with the techniques of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {N}$ </tex-math></inline-formula> -shift cipher and public key. Based on the Lyapunov stability sense and linear matrix inequality (LMI) framework, a new delay-dependent synchronization criterion is established to restore the original information signal on each node of the CDN as well as to ensure stable synchronization for secure communication of all nodes of the command system and CDN. With the support of numerical simulation, the validity of the proposed method is verified.

Stochastic Sampled-Data Exponential Synchronization of Markovian Jump Neural Networks With Time-Varying Delays.

In this article, the exponential synchronization of Markovian jump neural networks (MJNNs) with time-varying delays is investigated via stochastic sampling and looped-functional (LF) approach. For simplicity, it is assumed that there exist two sampling periods, which satisfies the Bernoulli distribution. To model the synchronization error system, two random variables that, respectively, describe the location of the input delays and the sampling periods are introduced. In order to reduce the conservativeness, a time-dependent looped-functional (TDLF) is designed, which takes full advantage of the available information of the sampling pattern. The Gronwall-Bellman inequalities and the discrete-time Lyapunov stability theory are utilized jointly to analyze the mean-square exponential stability of the error system. A less conservative exponential synchronization criterion is derived, based on which a mode-independent stochastic sampled-data controller (SSDC) is designed. Finally, the effectiveness of the proposed control strategy is demonstrated by a numerical example.

Adaptive Synchronization for Delayed Chaotic Memristor-Based Neural Networks.

This article considers the adaptive synchronization problem of delayed chaotic memristor-based neural networks (MNNs). Note that MNNs are modeled as continuous systems in the flux-voltage-time (ϕ,x,t) domain where memristors are viewed as continuous systems based on HP memristors. New adaptive controllers of MNNs are proposed, where controllers are both on memristors in the flux-time (ϕ,t) domain and neurons in the voltage-time (x,t) domain. Based on the Lyapunov method, Barbalat's lemma, differential mean value Theorem, and other inequality techniques, completed synchronization criteria for delayed chaotic MNNs are derived. In the end, two examples are given to demonstrate the validity of the derived results.

Cluster synchronization for directed coupled inertial reaction-diffusion neural networks with nonidentical nodes via non-reduced order method

The cluster synchronization issues are investigated for directed coupled inertial reaction-diffusion neural networks (CIRDNNs) with nonidentical nodes by imposing two effective pinning control. A novel Lyapunov-Krasovskii functional (LKF) is established to directly analyze the dynamic behavior of CIRDNNs and deal with reaction-diffusion term, inertia term and coupling term. Moreover, based on different desired cluster synchronization states including a set of un-decoupled trajectories and the particular solutions of the decoupled node systems, two class of synchronization criteria in view of algebraic inequalities are derived under two different communication topologies, respectively. Finally, two typical examples are given to verify the theoretical results.

Distributed synchronization of delayed dynamic networks under asynchronous delay-dependent impulsive control

In this paper, we investigate the distributed synchronization of delayed dynamic networks (DNs) with asynchronous delayed impulsive control. Compared with some related works, the design of delayed impulsive control input allows asynchronous actuation, which is more reasonable for distributed synchronization. The methods of average asynchronous impulsive interval and average asynchronous impulsive delay are used to effectively fetch the delay information existing in asynchronous impulses and integrated to the synchronization of delayed DNs. Some sufficient synchronization criteria for delayed DNs with/without delay are given by using mathematical induction and averaging method. The relationship among impulsive gain, average impulsive interval and average impulsive delays is discussed. The proposed pinning control acts at the asynchronous impulsive instants of the network nodes, which indicates that the time delays existing in asynchronous impulsive control input have a synchronizing effect on the synchronization of delayed DNs. Finally, typical networks are considered to show the validity of asynchronous delayed impulsive control approach.

Synchronization analysis of fractional delayed memristive neural networks via event-based hybrid impulsive controllers

In this paper, the asymptotic synchronization of Riemann–Liouville fractional delayed memristive neural networks is explored. Firstly, in order to achieve the control target more effectively and economically, a new type of event-based hybrid impulsive controller is designed. In addition, through inequality techniques and impulse analysis methods, some sufficient criteria for asymptotic synchronization are obtained by constructing new Lyapunov–Krasovskii functionals. At the same time, it is verified that Zeno behavior could be eliminated under the given trigger conditions in the error system. It should be noted that some results based on algebraic inequalities fill in the gaps of existing ones and our controller is more practical and energy-saving. Lastly, a simulation instance is depicted to verify the validity and correctness of the submitted conclusions.

Finite-time non-fragile control for synchronization of fractional-order stochastic neural networks

This study concerned with the synchronization problem over a finite-time domain for a class of fractional-order stochastic neural networks via non-fragile controller with discontinuous activation functions. Specifically, the suggested state feedback controller sequentially cope with non-fragile scheme for gain scheduling process. Notably, the main objective of this work is to obtained the finite-time synchronization criterion for the resulting synchronized error system over finite bound with the developed non-fragile controller. For that, some consignment of sufficient conditions is derived systematically by implementing Lyapunov’s indirect method and finite-time stability theory which ensures the finite-time stochastic synchronization of the stipulated neural networks. Later on, the controller gain fluctuations that obeying certain white noise sequels derived from Bernoulli distribution are formulated in terms of linear matrix inequalities. Eventually, the illustrated study are substantiated through two numerical examples and the simulation results manifest the advantage and accuracy of the proposed synchronization criteria.

Exponential [formula omitted] synchronization and anti-synchronization of delayed discrete-time complex-valued neural networks with uncertainties

This paper investigates the problem of exponential synchronization and anti-synchronization for uncertain discrete-time neural networks (NNs) having time-varying delays with H∞ performance in complex domain. An output-feedback controller is utilized not only to guarantee the synchronization criteria between the addressed discrete-time complex-valued neural networks (CVNNs) but also to reduce the effect of external disturbance. In order to assure the anti-synchronization criteria with H∞ performance for the proposed CVNNs, we have introduced the output-feedback controller by anti-synchronization error analysis. With the help of Lyapunov–Krasovskii functional (LKF), some linear matrix inequality (LMI) based sufficient conditions are derived for both synchronization and anti-synchronization criteria which can be validated through YALMIP toolbox in MATLAB software. At last, a numerical simulation result is provided to verify the correctness of the established theoretical results.

Predefined-time synchronization of coupled neural networks with switching parameters and disturbed by Brownian motion

This article focuses on predefined time synchronization problem for a class of signal switching neural networks with time-varying delays. In the network models, we not only consider the coupling characteristics in the following networks, but also consider the disturbance with standard Brownian motion. In the design of the controller, the control gain is designed as 1ɛ+Tp−t (t∈[T0,Tp), ɛ is an optional smaller positive number), which avoids the infinite gain (the control gain is designed as 1Tp−t in other reference). In order to get the predefined time control law, a power function is multiplied to the Lyapunov functional, from which it can get an exponential upper bound function via the derivative and mathematical expectation operation. Utilizing the martingale theory and the method of Laplace matrix, some novel predefined time synchronization criteria are obtained for the leader-following neural networks, meanwhile the following networks can maintain the leader network after achieved synchronization. Based on the special network of the main system, five corollaries separately develop the predefined time synchronization results from different perspectives. An example with some simulation figures and computing results fully exhibits the effectiveness of the achieved synchronization scheme. In this case, although the error signal is disturbed by Brownian motion, the trace signal can still stably converge to zero by this control scheme, meanwhile the predefined-time control effect is achieved.

Synchronization for Complex Networks With Multiple State or Delayed State Couplings Under Recoverable Attacks

In this article, we, respectively, take the synchronization into consideration for directed and undirected complex networks (CNs) with multiple state or delayed state couplings subject to recoverable attacks. By selecting appropriate Lyapunov functional, employing inequality techniques, and adopting the designed state-feedback controller, two criteria of the synchronization are established for the directed CN with multiple state couplings (CNMSCs). Moreover, the synchronization of CNMSCs is also discussed for the case that the network topology is undirected. In addition, two types of CNs with multiple delayed state couplings are also proposed, and several criteria of synchronization are formulated for these networks. Finally, two examples are given to verify the correctness of the derived synchronization criteria.

Distributed hierarchal control strategy for multi-bus AC microgrid to achieve seamless synchronization

• Pinning consensus-based controller is designed for seamless synchronization. • A natural conflict between the frequency and phase regulation has been resolved. • BP based PI controller is used to update the fixed gain parameters of SC. • FPI and SB based FLC are designed to generate the correction signals for SC. In this research work, a distributed hierarchal control scheme is proposed that ensures a smooth synchronization of islanded microgrid with the utility grid. In this method, a pinning consensus-based distributed controller is designed where all Distributed Generation Units (DGs) are allowed to regulate their frequencies and output power in proportion to their capacities while only regulating DGs are responsible for eliminating the phase angle and voltage magnitude mismatch. Hence, the magnitude, phase angle, and frequency are controlled explicitly while ensuring proportionate power sharing. To enhance the performance of the system, the fixed gain parameters of the secondary controller are made adaptive by using a back propagation based proportional integral controller. Moreover, a fuzzy proportional integral controller and steepest descent based fuzzy logic controller are designed that use an adjustable parameter to generate the compensation correction signals for the secondary controller to eliminate the voltage magnitude and phase angle mismatch. Furthermore, to ensure a seamless reconnection, a control strategy based on the synchronization criteria is designed that control the operation of the static switch. Finally, the effectiveness of the method under different scenarios is validated through simulation results.

Adaptive Fixed-Time Synchronization of Delayed Memristor-Based Neural Networks with Discontinuous Activations

Fixed-time synchronization (FTS) of delayed memristor-based neural networks (MNNs) with discontinuous activations is studied in this paper. Both continuous and discontinuous activations are considered for MNNs. And the mixed delays which are closer to reality are taken into the system. Besides, two kinds of control schemes are proposed, including feedback and adaptive control strategies. Based on some lemmas, mathematical inequalities and the designed controllers, a few synchronization criteria are acquired. Moreover, the upper bound of settling time (ST) which is independent of the initial values is given. Finally, the feasibility of our theory is attested by simulation examples.

Quantized Synchronization Control of Networked Nonlinear Systems: Dynamic Quantizer Design With Event-Triggered Mechanism.

This article investigates the quantized control issue for synchronizing a networked nonlinear system. Due to limited energy and channel resources, the event-triggered control (ETC) method and input quantization are simultaneously taken into account in this article. First, a dynamic quantizer, which discretely adjusts its parameters online and possesses a finite quantization range, is introduced to achieve exact synchronization, rather than quasisynchronization. Next, a new distributed Zeno-free ETC strategy is proposed based on the dynamic quantizer. Then, two different situations, that is, the quantizer is designed with/without the network topology information, are, respectively, discussed. Synchronization criteria are, respectively, derived under such two circumstances by using the Lyapunov method. Finally, numerical examples are provided to show the effectiveness of the theoretical results.

Passivity-based synchronization for switched dynamical networks with and without coupling time-varying delays

This paper investigates the passivity-based synchronization for switched dynamical networks (SDNs) with and without coupling time-varying delays. By utilizing the Lyapunov functional method, several sufficient conditions are derived to guarantee the passivity for SDNs, and the association between synchronization and passivity of the system is also revealed. In particular, both the cases that the SDNs are with and without coupling time-varying delays are tackled, wherein the synchronization criteria are derived. Finally, two illustrative numerical examples are exploited to verify the effectiveness of the passivity-based synchronization criteria and to demonstrate the advantage of the proposed approach.

AMPLITUDE CONTROL AND CHAOTIC SYNCHRONIZATION OF A COMPLEX-VALUED LASER RING NETWORK

Many real-world systems are connected together, in natural and man-made networks. A complex-valued laser network can simulate the working mechanism of human brain. However, amplitude control of a complex-valued laser network is seldom studied. In this paper, a ring network of complex-valued Lorenz laser systems is investigated. The ring network exhibits complex dynamics including hyper-chaos, quasi-periodic orbits, and coexisting hyper-chaos. Three kinds of single-parameter oriented amplitude controls are realized with varying or unvarying Lyapunov exponents in the ring network. Meanwhile, a simple knob can realize the amplitude rescaling of hyper-chaotic signals, which reduces the cost of circuit implementation. Moreover, a criterion of chaotic complete synchronization among all the nodes is established for a network with strong coupling. For relatively weak coupling, quasi-periodic complete synchronization is found, and the performance of chaotic synchronization is studied in terms of the cross-correlation coefficient. It is moreover revealed that the improvement and trend of synchronization performance are robust to the parity of the number of nodes for the same-scale laser networks.