Can neural networks with arbitrary delays be finite-timely synchronized?

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.

Finite-Time and Fixed-Time Synchronization of Quaternion-Valued Neural Networks With/Without Mixed Delays: An Improved One-Norm Method

In this article, the finite-time synchronization (FTSYN) of a class of quaternion-valued neural networks (QVNNs) with discrete and distributed time delays is studied. Furthermore, the FTSYN and fixed-time synchronization (FIXSYN) of the QVNNs without time delay are investigated. Different from the existing results, which used decomposition techniques, by introducing an improved one-norm, we use a direct analytical method to study the synchronization problems. Incidentally, several properties of one-norm of the quaternion are analyzed, and then, three effective controllers are proposed to synchronize the drive and response QVNNs within a finite time or fixed time. Moreover, efficient criteria are proposed to guarantee that the synchronization of QVNNs with or without mixed time delays can be realized within a finite and fixed time interval, respectively. In addition, the settling times are reckoned. Compared with the existing work, our advantages are mainly reflected in the simpler Lyapunov analytical process and more general activation function. Finally, the validity and practicability of the conclusions are illustrated via four numerical examples.

Finite-Time Synchronization of Markovian Coupled Neural Networks With Delays via Intermittent Quantized Control: Linear Programming Approach

This article is devoted to investigating finite-time synchronization (FTS) for coupled neural networks (CNNs) with time-varying delays and Markovian jumping topologies by using an intermittent quantized controller. Due to the intermittent property, it is very hard to surmount the effects of time delays and ascertain the settling time. A new lemma with novel finite-time stability inequality is developed first. Then, by constructing a new Lyapunov functional and utilizing linear programming (LP) method, several sufficient conditions are obtained to assure that the Markovian CNNs achieve synchronization with an isolated node in a settling time that relies on the initial values of considered systems, the width of control and rest intervals, and the time delays. The control gains are designed by solving the LP. Moreover, an optimal algorithm is given to enhance the accuracy in estimating the settling time. Finally, a numerical example is provided to show the merits and correctness of the theoretical analysis.

Finite-time bipartite synchronization of switched competitive neural networks with time delay via quantized control

This article tackles the finite-time bipartite synchronization (FTBS) of coupled competitive neural networks (CNNs) with switching parameters and time delay. Quantized control is utilized to achieve the FTBS at a small control cost and with limited channel resources. Since the effects of the time delay and switching parameters, traditional finite-time techniques cannot be directly utilized to the FTBS. By constructing a novel multiple Lyapunov functional (MLF), a sufficient criterion formulated by linear programming (LP) is established for the FTBS and the estimation of the settling time. To further improve the accuracy of the settling time, another MLF is designed by dividing the dwell time. With the aid of convex combination, a new LP is provided, which removes the requirement that the increment coefficient of the MLF at switching instants has to be larger than 1. In addition, to obtain the more precise settling time, an optimal algorithm is provided. Two numerical examples are put forward to demonstrate the reasonableness of the theoretical analysis.

Finite-time H∞ synchronization control for coronary artery chaos system with input and state time-varying delays

This is the first time for studying the issue of finite-time H_∞ synchronization control for the coronary artery chaos system (CACS) with input and state time-varying delays. Feedback control is planned for finite-time of synchronization CACS. By constructing the Lyapunov-Krasovskii functional (LKF) is derived for finite-time stability criteria of CACS with interval and continuous differential time-varying delays. We use Wirtinger-based integral inequality to evaluate the upper bound of the time derivative of the LKF. We apply the single integral form and the double integral form of the integral inequality, according to Wirtinger-based integral inequality, to ensure that the feedback controller for synchronization has good performance with disturbance and time-varying delay. The new sufficient finite-time stability conditions have appeared in the form of linear matrix inequalities (LMIs). Numerical checks can be performed using the LMI toolbox in MATLAB. A numerical example is presented to demonstrate the success of the proposed methods. This resultant is less conservative than the resultants available in the previous works.

Finite- and Fixed-Time Cluster Synchronization of Nonlinearly Coupled Delayed Neural Networks via Pinning Control

In this article, the cluster synchronization problem for a class of the nonlinearly coupled delayed neural networks (NNs) in both finite- and fixed-time cases are investigated. Based on the Lyapunov stability theory and pinning control strategy, some criteria are provided to ensure the cluster synchronization of the nonlinearly coupled delayed NNs in both finite-and fixed-time aspects. Then, the settling time for stabilization that is dependent on the initial value and independent of the initial value is estimated, respectively. Finally, we illustrate the feasibility and practicality of the results via a numerical example.

Fixed-Time Synchronization of Coupled Neural Networks With Discontinuous Activation and Mismatched Parameters

This article is concerned with fixed-time synchronization of the nonlinearly coupled neural networks with discontinuous activation and mismatched parameters. First, a novel lemma is proposed to study fixed-time stability, which is less conservative than those in most existing results. Then, based on the new lemma, a discontinuous neural network with mismatched parameters will synchronize to the target state within a settling time via two kinds of unified and simple controllers. The settling time is theoretically estimated, which is independent of the initial values of the considered network. In particular, the estimated settling time is closer to the real synchronization time than those given in the existing literature. Finally, two numerical simulations are presented to illustrate the effectiveness and correctness of our results.

Synchronization in Finite-Time Analysis of Clifford-Valued Neural Networks with Finite-Time Distributed Delays

In this paper, we explore the finite-time synchronization of Clifford-valued neural networks with finite-time distributed delays. To address the problem associated with non-commutativity pertaining to the multiplication of Clifford numbers, the original n-dimensional Clifford-valued drive and response systems are firstly decomposed into the corresponding 2m-dimensional real-valued counterparts. On the basis of a new Lyapunov–Krasovskii functional, suitable controller and new computational techniques, finite-time synchronization criteria are formulated for the corresponding real-valued drive and response systems. The feasibility of the main results is verified by a numerical example.

Synchronization of Coupled Time-Delay Neural Networks With Mode-Dependent Average Dwell Time Switching

In the literature, the effects of switching with average dwell time (ADT), Markovian switching, and intermittent coupling on stability and synchronization of dynamic systems have been extensively investigated. However, all of them are considered separately because it seems that the three kinds of switching are different from each other. This article proposes a new concept to unify these switchings and considers global exponential synchronization almost surely (GES a.s.) in an array of neural networks (NNs) with mixed delays (including time-varying delay and unbounded distributed delay), switching topology, and stochastic perturbations. A general switching mechanism with transition probability (TP) and mode-dependent ADT (MDADT) (i.e., TP-based MDADT switching in this article) is introduced. By designing a multiple Lyapunov-Krasovskii functional and developing a set of new analytical techniques, sufficient conditions are obtained to ensure that the coupled NNs with the general switching topology achieve GES a.s., even in the case that there are both synchronizing and nonsynchronizing modes. Our results have removed the restrictive condition that the increment coefficients of the multiple Lyapunov-Krasovskii functional at switching instants are larger than one. As applications, the coupled NNs with Markovian switching topology and intermittent coupling are employed. Numerical examples are provided to demonstrate the effectiveness and the merits of the theoretical analysis.

Finite-Time Synchronization of Markovian Jumping Complex Networks with Non-Identical Nodes and Impulsive Effects

In this paper, we investigate the finite-time synchronization problem for a class of Markovian jumping complex networks (MJCNs) with non-identical nodes and impulsive effects. Sufficient conditions for the MJCNs are presented based on an M-matrix technique, Lyapunov function method, stochastic analysis technique, and suitable comparison systems to guarantee finite-time synchronization. At last, numerical examples are exploited to illustrate our theoretical results, and they testify the effectiveness of our results for complex dynamic systems.

Finite-Time Synchronization of Discontinuous Neural Networks With Delays and Mismatched Parameters

This paper investigates the problem of finite-time drive-response synchronization for a class of neural networks with discontinuous activations, time-varying discrete and infinite-time distributed delays, and mismatched parameters. In order to cope with the difficulties induced by discontinuous activations, time delays, as well as mismatched parameters simultaneously, new 1-norm-based analytical techniques are developed. Both state feedback and adaptive controllers with and without the sign function are designed. Based on differential inclusion theory and Lyapunov functional method, several sufficient conditions on the finite-time synchronization are obtained. Our results show that the controllers with a sign function can reduce the conservativeness of control gains and the controllers without a sign function can overcome the chattering phenomenon. Numerical examples are given to show the effectiveness of the theoretical analysis.

Robust Finite-Time Stabilization of Fractional-Order Neural Networks With Discontinuous and Continuous Activation Functions Under Uncertainty

This paper is concerned with robust finite-time stabilization for a class of fractional-order neural networks (FNNs) with two types of activation functions (i.e., discontinuous and continuous activation function) under uncertainty. It is worth noting that there exist few results about FNNs with discontinuous activation functions, which is mainly because classical solutions and theories of differential equations cannot be applied in this case. Especially, there is no relevant finite-time stabilization research for such system, and this paper makes up for the gap. The existence of global solution under the framework of Filippov for such system is guaranteed by limiting discontinuous activation functions. According to set-valued analysis and Kakutani's fixed point theorem, we obtain the existence of equilibrium point. In particular, based on differential inclusion theory and fractional Lyapunov stability theory, several new sufficient conditions are given to ensure finite-time stabilization via a novel discontinuous controller, and the upper bound of the settling time for stabilization is estimated. In addition, we analyze the finite-time stabilization of FNNs with Lipschitz-continuous activation functions under uncertainty. The results of this paper improve corresponding ones of integer-order neural networks with discontinuous and continuous activation functions. Finally, three numerical examples are given to show the effectiveness of the theoretical results.

Finite time synchronization of memristor-based Cohen-Grossberg neural networks with mixed delays

Finite time synchronization, which means synchronization can be achieved in a settling time, is desirable in some practical applications. However, most of the published results on finite time synchronization don't include delays or only include discrete delays. In view of the fact that distributed delays inevitably exist in neural networks, this paper aims to investigate the finite time synchronization of memristor-based Cohen-Grossberg neural networks (MCGNNs) with both discrete delay and distributed delay (mixed delays). By means of a simple feedback controller and novel finite time synchronization analysis methods, several new criteria are derived to ensure the finite time synchronization of MCGNNs with mixed delays. The obtained criteria are very concise and easy to verify. Numerical simulations are presented to demonstrate the effectiveness of our theoretical results.

Synchronization of Delayed Memristive Neural Networks: Robust Analysis Approach

This paper considers the asymptotic and finite-time synchronization of drive-response memristive neural networks (MNNs) with time-varying delays. It is known that the parameters of MNNs are state-dependent, and hence the traditional robust control and analytical techniques cannot be directly applied. This difficulty is overcome by using the concept of Filippov solution. However, the special characteristics of MNNs may lead to unexpected parameter mismatch issue when different initial conditions are chosen. Based on a new robust control design, the mismatching issue is solved. Sufficient conditions are derived to guarantee the asymptotic synchronization of the considered MNNs with delays, which may be less conservative than synchronization criterion obtained by using existing methods. Moreover, without using the existing finite-time stability theorem, finite-time synchronization of the MNNs with delays is also investigated. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical analysis.

Finite-time synchronization of fractional-order memristor-based neural networks with time delays

In this paper, we consider the problem of finite-time synchronization of a class of fractional-order memristor-based neural networks (FMNNs) with time delays and investigated it potentially. By using Laplace transform, the generalized Gronwall's inequality, Mittag-Leffler functions and linear feedback control technique, some new sufficient conditions are derived to ensure the finite-time synchronization of addressing FMNNs with fractional order α:1<α<2 and 0<α<1. The results from the theory of fractional-order differential equations with discontinuous right-hand sides are used to investigate the problem under consideration. The derived results are extended to some previous related works on memristor-based neural networks. Finally, three numerical examples are presented to show the effectiveness of our proposed theoretical results.