Exponential Synchronization Research Articles

Intermittent event-triggered control for exponential synchronization of delayed neural networks on time Scales

This paper studies the exponential synchronization of delayed neural networks (DNNs) on time scales using the intermittent event-triggered control (IETC) method. Initially, considering the time scale situation, an IETC that merges intermittent control and event-triggered control is introduced, and a new differential inequality is developed. Subsequently, an exponential synchronization criterion is established based on the Lyapunov function, the proposed differential inequality and the time scale theory, applicable to continuous, discrete and hybrid time domains. Furthermore, under the event-triggered condition, it is demonstrated that the lower bound of each event-triggered interval exceeds a positive constant, thereby preventing the occurrence of Zeno’s behavior. Finally, the approach efficacy is validated through numerical examples.

Global exponential synchronization of BAM memristive neural networks with mixed delays and reaction–diffusion terms

Based on m-norm, this paper investigates global exponential synchronization (GES) for BAM memristive neural networks (BAMMNNs) with mixed delays and reaction–diffusion (RD) terms. Different from the existing literatures, this paper discusses the GES of the NNs based on a new integral inequality with infinite distributed delay. This method is based on inequality technique and comparison principle, which makes the form of Lyapunov function and controller more simple. Next, by introducing two different control strategies and the concept of driven response, two sufficient conditions are got to ensure GES of the proposed system. It is noteworthy that the results obtained by algebraic inequality are extension of the previous conclusions. Finally, two instances verify the correctness of the conclusions.

Nonfragile Exponential Synchronization for Delayed Fuzzy Memristive Inertial Neural Networks via Memory Sampled-Data Control

Nonfragile Exponential Synchronization for Delayed Fuzzy Memristive Inertial Neural Networks via Memory Sampled-Data Control

Global robust exponential synchronization of neutral-type interval Cohen–Grossberg neural networks with mixed time delays

Global robust exponential synchronization of neutral-type interval Cohen–Grossberg neural networks (NTICGNNs) with mixed time delays is analyzed in this paper. The system model, in which unrepresentable using vector-matrices, renders certain methods unsuitable for addressing issues within the vector-matrix framework. To address this limitation, a direct method based on system solutions is proposed, and sufficient conditions are provided to achieve global robust exponential synchronization of the considered NTICGNNs. This approach results in a global robust exponential synchronization criterion without the need to establish any Lyapunov-Krasovskii functionals. The applicability of the obtained synchronization conditions is validated using two numerical examples. Additionally, the obtained theoretical results have been applied to solve a quadratic programming problem and to encrypt and decrypt color images, demonstrating the practical application value of our research results. Notably, this study presents the first global robust exponential synchronization analysis for the considered NTICGNNs and proposes a novel approach grounded in system solutions.

Exponential Synchronization of Stochastic Time-delayed Memristor-based Neural Networks via Pinning Impulsive Control

Exponential Synchronization of Stochastic Time-delayed Memristor-based Neural Networks via Pinning Impulsive Control

Synchronization of delayed stochastic reaction–diffusion Hopfield neural networks via sliding mode control

Synchronization of stochastic reaction–diffusion Hopfield neural networks with s-delays via sliding mode control is investigated in this article. To begin with, we choose suitable functional space for state variables, then the system is transformed into a functional differential equation in an infinite-dimensional Hilbert space by using appropriate functional analysis technique. Based on above preliminary preparation, sliding mode control (SMC) is constructed to drive the error trajectory into the designed switching surface. Specifically, the switching surface is constructed as linear combination of state variables, which is related to control gains. Then novel SMC law is designed which involving delay, reaction diffusion term, and reaching law. Furthermore, the criterion of mean-square exponential synchronization for stochastic delayed reaction–diffusion Hopfield neural networks with s-delays is given in the form of matrix form. This criterion is less restrictive and easy to check in computer. Meanwhile, a different novel Lyapunov–Krasovskii functional (LKF) mixed with Itô’s formula, Young inequality, Hanalay inequality is employed in this proof procedure. At last, a numerical example is presented to validate the availability of theoretical result. The simulation is based on the finite difference method, and numerical result coincides with the theoretical result proposed.

Global exponential synchronization of complex networks with reaction diffusions and finite distributed delays coupling

This article investigates global exponential synchronization of complex networks with reaction diffusions and finite distributed delays coupling (RDDCCNs). Some restrictions on the coupling configuration matrix and time-varying delays are removed. By constructing comparison functions, utilizing analytic method and inequality techniques, a criterion for exponential synchronization of RDDCCNs is attained under adaptive intermittent control. A corresponding outcome without RDs is also acquired. At last, two simulations are proposed to illustrate validity of the obtained criteria.

Reachable set performance and quantized sampled-data synchronization analysis of neural networks under random packet dropouts via enhanced looped functional

The study aims to present the synchronization concerns of neural networks with stochastic packet dropouts utilizing a quantized memory sampled-data control (QMSDC) scheme and the problem of reachable set analysis (RSA) for NNs under the influence of external disturbances are discussed. To do this, a novel free-weighting matrix integral inequality (FWMII) is proposed with an augmented Lyapunov-functional. Furthermore, at this time, we show that the proposed inequality is less conservative due to the delay information. In the meantime, a novel enhanced looped function is created that utilizes not only sampling information but also incorporates both transmission delay information and a quantized sampling pattern. Next, using the proposed FWMII technique, several sufficient conditions in terms of linear matrix inequalities (LMIs) are derived to suggest how an augmented closed-loop system can achieves stochastic mean-square exponential synchronization under random packet loss situations. Finally, the proposed approach demonstrates its usefulness and superiority by comparing it with existing methods through numerical simulation of the secure communications.

Sampled-Data Control for Exponential Synchronization of Delayed Inertial Neural Networks With Aperiodic Sampling and State Quantization.

This article is devoted to dealing with exponential synchronization for inertial neural networks (INNs) with heterogeneous time-varying delays (HTVDs) under the framework of aperiodic sampling and state quantization. First, by taking the effect of aperiodic sampling and state quantization into consideration, a novel quantized sampled-data (QSD) controller with time-varying control gain is designed to tackle the exponential synchronization of INNs. Second, considering the available information of the lower and upper bounds of each HTVD, a refined Lyapunov-Krasovskii functional (LKF) is proposed. Meanwhile, an improved looped-functional method is utilized to fully capture the characteristic of practical sampling patterns and further relax the positive definiteness requirement for LKF. Consequently, less conservative exponential synchronization conditions with extra flexibility are derived. Finally, a numerical example is employed to demonstrate the effectiveness and advantages of the proposed synchronization method.

Exponential Synchronization of Markovian Jump Neural Networks Based on Asynchronous Delayed-Feedback Controller With Uncertain Hidden Information.

Due to the complex network environment, the feedback information cannot be timely received by the controller. This article proposes a method on the exponential synchronization for the Markovian jump neural networks, which is achieved by designing a new asynchronous delayed-feedback controller, with its feedback delay taken into account. The quantized relationship between the exponential synchronization and the feedback delay is derived from a new designed Lyapunov functional, to acquire delay boundaries. With the help of a hidden-Markov process, the designed controller shows asynchrony, which allows controller modes to run free. In particular, the detection probability is assumed to be bounded known, marking a breakthrough over existing results. Moreover, the proposed method proves to be applicable in both synchronous and asynchronous cases. By using the proposed method, the computation freedom of the controller gain matrix can be substantially augmented. Further, comparative numerical studies are implemented to validate the effectiveness and superiority of the proposed method.

Exponential synchronization of a class of quaternion-valued neural network with time-varying delays: A Matrix Measure Approach

This article investigates the exponential synchronization (ES) of quaternion-valued neural networks (QVNNs) with time-varying delays. Global ES has been studied using matrix measure techniques. Due to the incompatibility of quaternion multiplication, the QVNN system is first separated into four real-valued systems. Then ES is established in the master-response systems of QVNN by constructing a state feedback controller. The stability criteria for the error system of QVNN is then provided using the existing lemmas and the Halanay inequality. Additionally, it is no longer assumed that the activation functions are differentiable, which make the analytical process more concise. The viability of our findings are demonstrated using two numerical examples. The present theoretical findings have been confirmed in the first case, while the second example includes the use of QVNNs connected to associative memory to demonstrate their ability to restore real color image patterns properly.

Stability and Synchronization of Delayed Quaternion-Valued Neural Networks under Multi-Disturbances

This paper discusses a type of mixed-delay quaternion-valued neural networks (QVNNs) under impulsive and stochastic disturbances. The considered QVNNs model are treated as a whole, rather than as complex-valued neural networks (NNs) or four real-valued NNs. Using the vector Lyapunov function method, some criteria are provided for securing the mean-square exponential stability of the mixed-delay QVNNs under impulsive and stochastic disturbances. Furthermore, a type of chaotic QVNNs under stochastic and impulsive disturbances is considered using a previously established stability analysis method. After the completion of designing the linear feedback control law, some sufficient conditions are obtained using the vector Lyapunov function method for determining the mean-square exponential synchronization of drive–response systems. Finally, two examples are provided to demonstrate the correctness and feasibility of the main findings and one example is provided to validate the use of QVNNs for image associative memory.

H∞ Exponential Synchronization of Switched Cellular Neural Networks Based on Disturbance Observer-based Control

H∞ Exponential Synchronization of Switched Cellular Neural Networks Based on Disturbance Observer-based Control

New results on synchronization control of memristor-based quaternion-valued fuzzy neural networks with delayed impulses

A model of memristor-based quaternion-valued fuzzy neural networks (MQVFNNs) with delayed impulses and time-varying delays is established, and the synchronization issue is investigated in this paper. Firstly, to avoid non-commutativity, the MQVFNNs are decomposed into real-valued delayed impulsive neural networks. Secondly, a novel lemma for delayed impulsive system is introduced based on Halanay differential inequality. Then, by employing the theory of differential inclusion and the proposed lemma, some sufficient conditions are deduced to guarantee the global exponential synchronization of memristive quaternion-valued fuzzy neural networks under a simple delayed nonlinear control scheme. Finally, a numerical simulation is given to demonstrate the effectiveness of our theoretical results.

Global exponential synchronization of switching neural networks with leakage time-varying delays

In this paper, the synchronization problem of a class of switching neural networks with leakage time-varying delays is studied. A system solution-based direct analysis method is proposed to derive the sufficient conditions of global exponential synchronization for master–slave systems. Firstly, the state variable expression of the error system is derived by constructing a suitable regulation function, in which the leakage delays are explicitly transformed outside the state variable. Then, on this basis, the corresponding synchronization conditions is obtained by using the transition condition ingeniously. In addition, the obtained sufficient conditions contain only some simple linear scalar inequalities, which is different from most publications and greatly reduces the computational complexity. Finally, the reliability of the theoretical results is verified by numerical simulation. It is worth noting that the synchronization problem of switching neural networks with time-varying leakage delays is studied for the first time in this paper, and the method adopted does not need to construct any Lyapunov–Krasovskii functionals, which simplifies the proof process.

Exponential synchronization of complex networks via intermittent dynamic event-triggered control

In this paper, the exponential synchronization in mean square (ESMS) of complex networks (CNs) under intermittent dynamic event-triggered control strategy (IE-TCS) is discussed. Compared with the existing literature, the intermittent control strategy (ICS) proposed is awakened when a certain situation occurs rather than periodically, which can better improve the control efficiency. The average control rate in this paper is more flexible. Furthermore, we give a positive lower bound for the event-triggered intervals to ensure that Zeno behavior does not occur. Combining the graph-theoretic approach with the Lyapunov method, some criteria for ESMS are obtained. In particular, we also discuss the ESMS of non-strongly connected CNs under IE-TCS. Besides, we combine the self-triggered control strategy (S-TCS) with the ICS, which is called the intermittent S-TCS, to study the ESMS of CNs. For practicability, the theoretical results are applied to research the ESMS of the microgrid system, and some relevant sufficient conditions are derived. Eventually, numerical simulations are put forward to verify the effectiveness of theoretical results.

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.

Exponentially Synchronous Results for Delayed Neural Networks With Leakage Delay via Switched Delay Idea and AED-ADT Method.

Time delay has always been one of the main factors affecting the application performance of neural network (NN) systems, and dynamic performance research of NNs with time delays has been the focus of many scholars in recent years. This article enquires into the exponentially synchronous problem of switched delayed NNs with time delay in the leakage term. Adopting an unusual form from a common switched system, the switching modes of the switched delayed NNs system in this article are dependent on time delays. In the first place, the master, slave, and error NNs models are reconstructed into the switched form by introducing the switched delay idea. Then with the help of the admissible edge-dependent average dwell time (AED-ADT) method and delay-dependent switching adjustment indicators, a novel set of generalized delay-mode-dependent multiple Lyapunov-Krasovskii functionals (MLKFs) is built for analyzing the cases where a state-feedback controller exists and does not exist in the model, and where parts of LKFs may increase during the period when the corresponding subsystems are activated. For these cases, several effective exponential synchronization criteria and switching laws are presented accordingly. At last, the verification of the theoretical results is shown through a few examples.

Exponential Output Synchronization of Complex Networks With Output Coupling via Intermittent Event-Triggered Control

This paper considers the exponential output synchronization of complex networks with output coupling (CNOC) based on the intermittent event-triggered control (IE-TC) strategy. Unlike existing intermittent control strategies, the proposed IE-TC strategy is event-triggered instead of time-triggered during the control intervals. Moreover, the average control rate is adopted for intermittent control, which makes the results less conservative. A new Lyapunov function is proposed to simplify the proof, which does not require the traditional mathematical induction method for intermittent control. Based on the Lyapunov method and inequality technique, sufficient conditions for achieving exponential output synchronization of CNOC for undirected graph and digraph topologies are given, respectively. Moreover, the Zeno phenomenon can be excluded. Finally, an example with simulations is provided to verify the feasibility of the theoretical results.

Quasi-Synchronization of Fractional Multiweighted Coupled Neural Networks via Aperiodic Intermittent Control.

This article investigates the quasi-synchronization for fractional multiweighted coupled neural networks (FMCNNs) with discontinuous activation functions and mismatched parameters. First, under the generalized Caputo fractional-order derivative operator, a novel piecewise fractional differential inequality is established to study the convergence of fractional systems, which significantly extends some related published results. Subsequently, by exploiting the new inequality and Lyapunov stability theory, some sufficient quasi-synchronization conditions of FMCNNs are presented by aperiodic intermittent control. Meanwhile, the exponential convergence rate and synchronization error's bound are given explicitly. Finally, the validity of theoretical analysis is confirmed by numerical examples and simulations.