Global Exponential Synchronization Research Articles

Synchronization of Switched Neural Networks via Attacked Mode-Dependent Event-Triggered Control and Its Application in Image Encryption.

It is challenging to synchronize switched time-delay systems when some modes are uncontrolled and the dwell time (DT) of controlled mode is very small. Therefore, in this article, global exponential synchronization almost surely (GES a.s.) in a cluster of switched neural networks (NNs) with hybrid delays (time-varying delay and infinite-time distributed delay) is investigated, where transition probability (TP)-based random mode-dependent average DT (MDADT) switching is considered. A novel mode-dependent pinning event-triggered controller with nonidentical deception attacks is proposed to save the communication resource and derive less conservative results. The two necessary and restrictive conditions in existing papers that the value of the Lyapunov-Krasovskii functional (LKF) before switching instants should be smaller than that after corresponding instant and the DT of each switching mode is restricted by the sampling intervals of the event trigger are moved. Sufficient conditions in terms of linear matrix inequalities (LMIs) are given to guarantee the GES a.s., even though both synchronizing and nonsynchronizing modes coexist and maybe the minimum DT of synchronizing modes is very small. Numerical examples, including image encryption, are provided to demonstrate the merits of the new technique.

Asymptotically almost periodic synchronization in fuzzy competitive neural networks with Caputo-Fabrizio operator

This paper researches a class of Caputo-Fabrizio fractional-order fuzzy competitive neural networks (CF-FCNNs) with different time scales and time delays. Firstly, according to Banach contracting mapping principle and some appropriate assumptions, it derives CF-FCNNs possess a unique weak solution. Then, exponential Euler difference scheme of discrete-time CF-FCNNs (DCF-FCNNs) is presented by the constant variation methods and the difference format is implicit Euler difference and is solved by fractional PECE algorithm. Next, the existence of a unique bounded asymptotically almost periodic sequence solution, global exponential stability and synchronization of DCF-FCNNs are considered. In the end, numerical examples are given to describe the effectiveness of the acquired conclusions.

Synchronization of switched complex dynamical networks with impulses: state-dependent switching approach

This paper studies the globally exponential synchronization (GES) of a class of complex dynamical networks (CDNs) with switching topology involving impulse action. A novel state-dependent switching (SDS) approach to tune the switching topology of CDNs is designed based on the information of the node dynamics with impulses. Different from the traditional SDS results which are based on continuous state space, some sufficient conditions for network synchronization based on SDS are proposed in the framework of impulse action. A relationship between impulse action, the network structure, and switching topology is established, which is crucial to design the SDS law. Two different impulse actions on the network dynamics are fully considered in this paper, namely, stabilizing continuous dynamics with desynchronizing impulses and destabilizing continuous dynamics with synchronizing impulses. Finally, two numerical simulations are given to demonstrate the effectiveness of the proposed control method.

Direct approach-based synchronization of fully quaternion-valued neural networks with inertial term and time-varying delay

In this article, the global exponential and asymptotic synchronization for a type of quaternion-valued inertial delayed neural networks (QIDNNs) are explored by introducing a direct analysis approach. Above all, without reducing the order or decomposing the models of QIDNNs, a compact quaternion-valued control scheme is developed to ensure synchronization. In addition, two new Lyapunov functionals are constructed directly and several compact criteria represented by matrix inequalities are derived by means of the theory of quaternion and inequality technique. Furthermore, a quaternion-valued adaptive control law is proposed to automatically determine the control costs, and the synchronization is guaranteed by the aid of Barbalat Lemma. Lastly, the derived results are affirmed via a numerical example.

Event-triggered synchronization of a two-layer heterogeneous neural network via hybrid control

Multi-layer network contains multiple subsystems and different types of interaction, which is more practical than traditional single-layer network. On this observation, this paper explores point-to-point quasi-synchronization in a two-layer heterogeneous neural network system. The sufficient conditions for global exponential synchronization in the driving layer are given a coupling term. Based on the global exponential synchronization in the driver layer, this paper further studies the global point-to-point quasi-synchronization between the driver layer and the response layer of the two-layer neural network under the hybrid control and event-triggered control. Under this hybrid control strategies, the event can be activated if and only if the trigger condition is violated and the dynamical adaptive control is also involved. Moreover, the Zeno behavior under this strategy is eliminated by Lyapunov method and matrix theory. Finally, a numerical example is given to verify the theoretical results.

Exponential synchronization of quaternion‐valued memristor‐based neural networks with time‐varying delays

SummaryIn this paper, the global exponential synchronization of quaternion‐valued memristor‐based neural networks with time‐varying delays is discussed. Firstly, by using the differential inclusion theory and the set‐valued map theory, the discontinuous quaternion‐valued memristive neural networks is transformed into an uncertain system with interval parameters. A novel controller is designed to achieve the control goal. With the ‐measure method and Halanay inequality, the criterion for global exponential synchronization of the quaternion‐valued memristive neural networks is given. At last, a numerical simulation is given to prove the validity of the main results.

Global Exponential Stability and Synchronization of Discrete-Time Fuzzy Bidirectional Associative Memory Neural Networks via Mittag-Leffler Difference Approach

Global Exponential Stability and Synchronization of Discrete-Time Fuzzy Bidirectional Associative Memory Neural Networks via Mittag-Leffler Difference Approach

ALMOST PERIODIC SYNCHRONIZATION FOR COMPLEX-VALUED NEURAL NETWORKS WITH TIME-VARYING DELAYS AND IMPULSIVE EFFECTS ON TIME SCALES

We propose a class of complex-valued neural networks with timevarying delays and impulsive effects on time scales. By employing the Banach fixed point theorem and differential inequality technique on time scales, we obtain the existence of almost periodic solutions for this networks. Then, by constructing a suitable Lyapunov function, we obtain that the drive-response structure of complex-valued neural networks with almost periodic coefficients can realize the global exponential synchronization. Our results are completely new. Finally, we give an example to illustrate the feasibility of our results.

ANTI-PERIODIC SYNCHRONIZATION OF CLIFFORD-VALUED NEUTRAL-TYPE CELLULAR NEURAL NETWORKS WITH <i>D</i> OPERATOR

This paper explores a class of delayed Clifford-valued neutral-type cellular neural networks with a <i>D</i> operator. Considering that the multiplication of Clifford algebras does not satisfy the commutativity, by applying the non-decomposition method, Krasnoselskii’s Fixed Point Theorem and the proof by contradiction, we obtain several sufficient conditions for the existence and global exponential synchronization of anti-periodic solutions for Cliffordvalued neutral-type cellular neural networks with a <i>D</i> operator. Finally, we give one example to illustrate the feasibility and effectiveness of the main results.

时滞递归神经网络的全局指数同步

时滞递归神经网络的全局指数同步

Global exponential bipartite synchronization for neutral memristive inertial coupling mixed time-varying delays neural networks with antagonistic interactions

In this paper, the global exponential bipartite synchronization (GEBS) for neutral-type memristive inertial coupling mixed time-varying delays neural networks (NTMI-CMTVDNNs) with synergistic and antagonistic interactions (SAI) is investigated. Firstly, the NTMI-CMTVDNNs with SAI between neurons are modeled by a signed graph. Inertial network is equivalently transformed into the first-order differential equations via variable substitution. Secondly, a novel lemma is proposed to deal with parameter mismatch of the above modeled network. By designing delay-dependent and delay-independent discontinuous control laws, the delay-dependent sufficient conditions under the bounded and unbounded activation functions are obtained to ensure the GEBS of the NTMI-CMTVDNNs with SAI with or without a leader neurons, respectively. Finally, two numerical simulation examples illustrate the validity of our theoretical results.

Global exponential synchronization of discrete-time high-order switched neural networks and its application to multi-channel audio encryption

For a class of discrete-time high-order switched neural networks with time-varying delays, the global exponential synchronization (GES) problem and its application in audio encryption are addressed. In this work, the state feedback controllers are designed to ensure the GES of response and drive systems, and the controller gains are directly computed by the network parameters. Then, a numerical example is presented to explain the correctness of the synchronization theory. Moreover, a technique to audio encryption/decryption is proposed, and it is applied to a practical example to verify the applicability of the technique. The advantages of this paper are as follows: (i) GES criterion containing a group of simple matrix inequalities is established without the construction of a Lyapunov–Krasovskii functional (LKF), which is not always obvious; (ii) the controller gains are directly represented by the parameters in the network, and then it is easy to apply them to the audio encryption.

Secure Synchronization of Coupled Systems via Double Event-Triggering Mechanisms With Actuator Fault

This paper studies the global exponential synchronization almost surely (GES a.s.) for coupled systems (CSs) with stochastic switching topology by using event-based output feedback control. It is assumed that the sensor-controller channel is subject to stochastic deception attacks and the actuator faults may occur to some modes. Novel double mode-dependent adaptive event-triggering mechanisms (ETMs) are introduced based on sampled data technique. Not only the Zeno phenomenon is naturally excluded, but also the asynchronous phenomenon is skillfully avoided. Based on the Lyapunov-Krasovskii functional method and the linear matrix inequality (LMI) technology, some sufficient conditions are presented to guarantee GES a.s. of the concerned system. Moreover, the event-based output feedback controller and the double ETMs can be designed by solving LMIs. In addition, an event-based pinning control is considered and some sufficient conditions are presented. As a theoretic application, our proposed results can be applied to secure synchronization problem for CSs subject to stochastic mixed attacks consisting of denial-of-service (DoS) attacks and deception attacks. Finally, two numerical examples are presented to demonstrate the effectiveness and the merits of the theoretical analysis.

Synchronization of delayed complex dynamical networks with actuator failure by event-triggered pinning control

This paper investigates the synchronization problem of delayed complex dynamical networks (DCDNs) with actuator failure under dynamical event-triggered pinning control (ETPC). Firstly, the fault-tolerant control system (FTCS) based on pinning control is introduced for DCDNs with time-varying actuator faults, which can reduce the cost of synchronization control. By setting internal dynamical variables, a new event-triggered control (ETC) strategy is designed. Then, it is proved that this control scheme can not only ensure global exponential synchronization of DCDNs based on Lyapunov theory, but also effectively avoid Zeno behavior and can reduce the burden on networks communication. At last, a simulation example verifies the reliability of the introduced dynamical ETPC strategy.

Almost Anti-Periodic Oscillation Excited by External Inputs and Synchronization of Clifford-Valued Recurrent Neural Networks

The main purpose of this paper was to study the almost anti-periodic oscillation caused by external inputs and the global exponential synchronization of Clifford-valued recurrent neural networks with mixed delays. Since the space consists of almost anti-periodic functions has no vector space structure, firstly, we prove that the network under consideration possesses a unique bounded continuous solution by using the contraction fixed point theorem. Then, by using the inequality technique, it was proved that the unique bounded continuous solution is also an almost anti-periodic solution. Secondly, taking the neural network that was considered as the driving system, introducing the corresponding response system and designing the appropriate controller, some sufficient conditions for the global exponential synchronization of the driving-response system were obtained by employing the inequality technique. When the system we consider degenerated into a real-valued system, our results were considered new. Finally, the validity of the results was verified using a numerical example.

Stability analysis and synchronized control of fuzzy Mittag-Leffler discrete-time genetic regulatory networks with time delays

Exponential Euler differences for semi-linear differential equations of first order have got rapid development in the past few years and a variety of exponential Euler difference methods have become very significant researching topics. In allusion to fuzzy genetic regulatory networks of fractional order, this paper firstly establishes a novel difference method called Mittag-Leffler Euler difference, which includes the exponential Euler difference. In the second place, the existence of a unique global bounded solution and equilibrium point, global exponential stability and synchronization of the derived difference models are investigated. Compared with the classical fractional Euler differences, fuzzy Mittag-Leffler discrete-time genetic regulatory networks can better depict and retain the dynamic characteristics of the corresponding continuous-time models. What’s more important is that it starts a new avenue for studying discrete-time fractional-order systems and a set of theories and methods is constructed in studying Mittag-Leffler discrete models.

Exponential synchronization for second-order switched quaternion-valued neural networks with neutral-type and mixed time-varying delays

This article focuses on the global exponential synchronization (GES) for second-order state-dependent switched quaternion-valued neural networks (SOSDSQVNNs) with neutral-type and mixed delays. By proposing some new Lyapunov–Krasovskii functionals (LKFs) and adopting some inequalities, several new criteria in the shape of algebraic inequalities are proposed to ensure the GES for the concerned system by using hybrid switched controllers (HSCs). Different from the common reducing order and separation ways, this article presents some new LKFs to straightway discuss the GES of the concerned system based on non-reduction order and nonseparation strategies. Ultimately, an example is provided to validate the effectiveness of the theoretical outcomes.

Distributed Synchronization of Delayed Neural Networks: Delay-Dependent Hybrid Impulsive Control

In this paper, synchronization of coupled neural networks is investigated via distributed delayed impulsive control, and system delays, coupling delays and impulsive delays are simultaneously considered. Firstly, the concept of average delayed impulsive weight is proposed, which allows impulsive weights and impulsive delays to be integrated into just one expression, and afterward hybrid impulses can be augmented. Then, this paper extends the comparison principle by taking delayed impulses into account, where the limitation that system delays exist between two consecutive impulsive instants is released. Without any restriction on time delays, sufficient conditions of global exponential synchronization for coupled neural networks are obtained. Additionally, the corresponding convergence rate is estimated. It indicates that the networks can still achieve synchronization even if the impulses work negatively, or may destroy synchronization. Finally, three typical networks are investigated to verify the availability of the control schemes.

Synchronization issue of coupled neural networks based on flexible impulse control

The global exponential synchronization issue of coupled neural networks with time-delayed impulses is investigated in this paper. On the basis of the characteristics of coupled neural networks and theorems, we have built a novel coupled systems model. In order to fit the real situation, the impulses are flexible and it can beyond the impulsive interval under certain conditions in this paper. Therefore, our results are less restrictive and more practical compared to existing research. Besides, by using average impulsive delay (AID) and average impulsive interval (AII), we investigate two different effects of impulses on synchronization respectively and get a few adequate conditions for different types of synchronization. Finally, there are two examples of numerical simulations presented to illustrate the efficiency of the conclusions.

Network synchronization under distributed delayed impulsive control: Average delayed impulsive weight approach

This paper mainly investigates synchronization of complex dynamical networks (CDNs) with both system delay and coupled delay through distributed delayed impulsive control. Instead of constraining the impulsive weight and impulsive delay one by one, a new concept of average delayed impulsive weight is proposed to obtain more relaxed conditions. Subsequently, based on the impulsive control topology, Lyapunov theory and linear matrix inequality (LMI) design, certain flexible criteria of global exponential synchronization (GES) are given and the corresponding convergence rate is estimated. It is interesting to see that the CDNs can still achieve synchronization under comprehensive conditions though impulsive weights work negatively. Namely, the delays in impulsive control are able to promote synchronization potentially. Finally, simulations are given to show that the distributed delayed impulsive control can not only speeds up the convergence rate for synchronized networks, but also facilitates synchronization for desynchronized networks. In addition, the obtained results can be applied to unmanned craft systems.