New algebraic criteria for synchronization stability of chaotic memristive neural networks with time-varying delays

Adaptive Intermittent Pinning Control for Synchronization of Delayed Nonlinear Memristive Neural Networks With Reaction-Diffusion Items

In this article, the global exponential synchronization problem is investigated for a class of delayed nonlinear memristive neural networks (MNNs) with reaction-diffusion items. First, using the Green formula, Lyapunov theory, and proposing a new fuzzy adaptive pinning control scheme, some novel algebraic criteria are obtained to ensure the exponential synchronization of the concerned networks. Furthermore, the corresponding control gains can be promptly adjusted based on the current states of partial nodes of the networks. Besides, a fuzzy adaptive aperiodically intermittent pinning control law is also designed to synchronize the fuzzy MNNs (FMNNs). The controller with intermittent mechanism can obtain appropriate rest time and save energy consumption. Finally, some numerical examples are provided to confirm the effectiveness of the results in this article.

Adaptive Synchronization of Reaction-Diffusion Neural Networks With Nondifferentiable Delay via State Coupling and Spatial Coupling

In this article, master-slave synchronization of reaction-diffusion neural networks (RDNNs) with nondifferentiable delay is investigated via the adaptive control method. First, centralized and decentralized adaptive controllers with state coupling are designed, respectively, and a new analytical method by discussing the size of adaptive gain is proposed to prove the convergence of the adaptively controlled error system with general delay. Then, spatial coupling with adaptive gains depending on the diffusion information of the state is first proposed to achieve the master-slave synchronization of delayed RDNNs, while this coupling structure was regarded as a negative effect in most of the existing works. Finally, numerical examples are given to show the effectiveness of the proposed adaptive controllers. In comparison with the existing adaptive controllers, the proposed adaptive controllers in this article are still effective even if the network parameters are unknown and the delay is nonsmooth, and thus have a wider range of applications.

Discontinuous Event-Triggered Control for Local Stabilization of Memristive Neural Networks With Actuator Saturation: Discrete- and Continuous-Time Lyapunov Methods

In this article, the local stabilization problem is investigated for a class of memristive neural networks (MNNs) with communication bandwidth constraints and actuator saturation. To overcome these challenges, a discontinuous event-trigger (DET) scheme, consisting of the rest interval and work interval, is proposed to cut down the triggering times and save the limited communication resources. Then, a novel relaxed piecewise functional is constructed for closed-loop MNNs. The main advantage of the designed functional consists in that it is positive definite only in the work intervals and the sampling instants but not necessarily inside the rest intervals. With the aid of extended reciprocally convex combination lemma, generalized sector condition, and some inequality techniques, two local stabilization criteria are established on the basis of both the discrete- and continuous-time Lyapunov methods. The proposed analysis technique fully takes advantage of the looped-functional and the event-trigger mechanism. Moreover, two optimization schemes are, respectively, established to design the control gain and enlarge the estimates of the admissible initial conditions (AICs) and the upper bound of rest intervals. Finally, some comparison results are given to validate the superiority of the proposed method.

Finite-time synchronization of reaction-diffusion memristive neural networks: A gain-scheduled integral sliding mode control scheme

The finite-time synchronization issue of reaction-diffusion memristive neural networks (RDMNNs) is studied in this paper. To better synchronize the parameter-varying drive and response systems, an innovative gain-scheduled integral sliding mode control scheme is proposed, where the 2ⁿ controller gains can be scheduled and an integral switching surface function that contains a discontinuous term is involved. Moreover, by constructing a novel Lyapunov-Krasovskii functional and combining reciprocally convex combination (RCC) method, a less conservative finite-time synchronization criterion for RDMNNs is derived in the form of linear matrix inequalities (LMIs). Finally, three numerical simulations are exploited to illustrate the effectiveness, superiority and practicability of this paper.

Passivity and Dissipativity of Fractional-Order Quaternion-Valued Fuzzy Memristive Neural Networks: Nonlinear Scalarization Approach

In this article, the problem of passivity and dissipativity analysis is investigated for a class of fractional-order quaternion-valued fuzzy memristive neural networks. Based on the famous nonlinear scalarizing function, a nonlinear scalarization method is developed, which can be employed to compare the "size" of two different quaternions. In this way, the convex closure proposed by the quaternion-valued connection weights is meaningful. By constructing proper Lyapunov functional, several improved passivity criteria and dissipativity conclusions are established, which can be checked efficiently by utilizing some standard mathematical calculations. Finally, the obtained results are validated by simulation examples.

Global Exponential Stability of Memristive Neural Networks With Mixed Time-Varying Delays

This article investigates the Lagrange exponential stability and the Lyapunov exponential stability of memristive neural networks with discrete and distributed time-varying delays (DMNNs). By means of inequality techniques, theories of the M-matrix, and the comparison strategy, the Lagrange exponential stability of the underlying DMNNs is considered in the sense of Filippov, and the globally exponentially attractive set is estimated through employing the M-matrix and external input. Especially, when the external input is not concerned, the Lyapunov exponential stability of the corresponding DMNNs is developed immediately in the form of an M-matrix, which contains some published outcomes as special cases. Furthermore, by constructing an M-matrix-based differential system, the Lyapunov exponential stability of the DMNNs is studied, which is less conservative than some existing ones. Finally, three simulation examples are carried out to examine the validness of the theories.

Bipartite Synchronization of Multiple Memristor-Based Neural Networks With Antagonistic Interactions

In this article, by introducing a signed graph to describe the coopetition interactions among network nodes, the mathematical model of multiple memristor-based neural networks (MMNNs) with antagonistic interactions is established. Since the cooperative and competitive interactions coexist, the states of MMNNs cannot reach complete synchronization. Instead, they will reach the bipartite synchronization: all nodes' states will reach an identical absolute value but opposite sign. To reach bipartite synchronization, two kinds of the novel node- and edge-based adaptive strategies are proposed, respectively. First, based on the global information of the network nodes, a node-based adaptive control strategy is constructed to solve the bipartite synchronization problem of MMNNs. Secondly, a local edge-based adaptive algorithm is proposed, where the weight values of edges between two nodes will change according to the designed adaptive law. Finally, two simulation examples validate the effectiveness of the proposed adaptive controllers and bipartite synchronization criteria.

Global Stabilization of Fuzzy Memristor-Based Reaction-Diffusion Neural Networks

This article investigates the global stabilization problem of Takagi-Sugeno fuzzy memristor-based neural networks with reaction-diffusion terms and distributed time-varying delays. By using the Green formula and proposing fuzzy feedback controllers, several algebraic criteria dependent on the diffusion coefficients are established to guarantee the global exponential stability of the addressed networks. Moreover, a simpler stability criterion is obtained by designing an adaptive fuzzy controller. The results derived in this article are generalized and include some existing ones as special cases. Finally, the validity of the theoretical results is verified by two examples.

Proportional-Integral Observer Design for Multidelayed Sensor-Saturated Recurrent Neural Networks: A Dynamic Event-Triggered Protocol

In this article, the design problem of the proportional-integral observer (PIO) is investigated for a class of discrete-time multidelayed recurrent neural networks (RNNs). In the addressed RNN model, the delays occurring in the information interconnections are allowed to be different, and the phenomenon of sensor saturation is taken into consideration in the measurement model. A novel dynamic event-triggered protocol is employed in the data transmission from sensors to the observer with hope to improve the efficiency of resource utilization, where the threshold parameters are adaptive to the dynamical environment. By virtue of the Lyapunov-like approach, a general framework is established for examining the boundedness of the estimation errors in mean-square sense, and the ultimate bound of the error dynamics is also acquired. Subsequently, the explicit expression of the desired PIO is parameterized by using the matrix inequality techniques. Finally, a simulation example is utilized to verify the effectiveness and superiority of the proposed PIO design scheme.

Synchronization of Memristive Complex-Valued Neural Networks With Time Delays via Pinning Control Method

This article concentrates on the synchronization problem of memristive complex-valued neural networks (CVNNs) with time delays via the pinning control method. Different from general control schemes, the pinning control is beneficial to reduce the control cost by pinning the fractional nodes instead of all ones. By separating the complex-valued system into two equivalent real-valued systems and employing the Lyapunov functional as well as some inequality techniques, the asymptotic synchronization criterion is given to guarantee the realization of synchronization of memristive CVNNs. Meanwhile, sufficient conditions for exponential synchronization of the considered systems is also proposed. Finally, the validity of our proposed results is verified by a numerical example.

Lagrange Stability and Finite-Time Stabilization of Fuzzy Memristive Neural Networks With Hybrid Time-Varying Delays

This paper focuses on Lagrange exponential stability and finite-time stabilization of Takagi-Sugeno (T-S) fuzzy memristive neural networks with discrete and distributed time-varying delays (DFMNNs). By resorting to theories of differential inclusions and the comparison strategy, an algebraic condition is developed to confirm Lagrange exponential stability of the underlying DFMNNs in Filippov's sense, and the exponentially attractive set is estimated. When external input is not considered, global exponential stability of DFMNNs is derived directly, which includes some existing ones as special cases. Furthermore, finite-time stabilization of the addressed DFMNNs is analyzed by exploiting inequality techniques and the comparison approach via designing a nonlinear state feedback controller. The boundedness assumption of activation functions is removed herein. Finally, two simulations are presented to demonstrate the validness of the outcomes, and an application is performed in pseudorandom number generation.

Adaptive Synchronization of Reaction-Diffusion Neural Networks and Its Application to Secure Communication

This paper is mainly concerned with the synchronization problem of reaction-diffusion neural networks (RDNNs) with delays and its direct application in image secure communications. An adaptive control is designed without a sign function in which the controller gain matrix is a function of time. The synchronization criteria are established for an error model derived from master-slave models through solving the set of linear matrix inequalities derived by constructing the suitable novel Lyapunov-Krasovskii functional candidate, Green's formula, and Wirtinger's inequality. If the proposed sufficient conditions are satisfied, then the global asymptotic synchronization of the error model is guaranteed. The numerical illustrations are provided to demonstrate the validity of the derived synchronization criteria. In addition, the role of system parameters is picturized through the chaotic nature of RDNNs and those unprecedented solutions is utilized to promote better security of image transactions. As is evident, the enhancement of image encryption algorithm is designed with two levels, namely, image watermarking and diffusion process. The contributions of this paper are discussed as concluding remarks.

A Switched Operation Approach to Sampled-Data Control Stabilization of Fuzzy Memristive Neural Networks With Time-Varying Delay

This paper investigates the issue of sampled-data stabilization for Takagi-Sugeno fuzzy memristive neural networks (FMNNs) with time-varying delay. First, the concerned FMNNs are transformed into the tractable fuzzy NNs based on the excitatory and inhibitory of memristive synaptic weights using a new convex combination technique. Meanwhile, a switched fuzzy sampled-data controller is employed for the first time to tackle stability problems related to FMNNs. Then, the novel stabilization criteria of the FMNNs are established using the fuzzy membership functions (FMFs)-dependent Lyapunov-Krasovskii functional. This sufficiently utilizes information from not only the delayed state and the actual sampling pattern but also the FMFs. Two simulation examples are presented to demonstrate the feasibility and validity of the proposed method.

On the validity of memristor modeling in the neural network literature

An analysis of the literature shows that there are two types of non-memristive models that have been widely used in the modeling of so-called "memristive" neural networks. Here, we demonstrate that such models have nothing in common with the concept of memristive elements: they describe either non-linear resistors or certain bi-state systems, which all are devices without memory. Therefore, the results presented in a significant number of publications are at least questionable, if not completely irrelevant to the actual field of memristive neural networks.

Exponential Stabilization of Fuzzy Memristive Neural Networks With Hybrid Unbounded Time-Varying Delays

This paper is concerned with exponential stabilization for a class of Takagi-Sugeno fuzzy memristive neural networks (FMNNs) with unbounded discrete and distributed time-varying delays. Under the framework of Filippov solutions, algebraic criteria are established to guarantee exponential stabilization of the addressed FMNNs with hybrid unbounded time delays via designing a fuzzy state feedback controller by exploiting inequality techniques, calculus theorems, and theories of fuzzy sets. The obtained results in this paper enhance and generalize some existing ones. Meanwhile, a general theoretical framework is proposed to investigate the dynamical behaviors of various neural networks with mixed infinite time delays. Finally, two simulation examples are performed to illustrate the validity of the derived outcomes.

Quasi-Synchronization of Delayed Chaotic Memristive Neural Networks

We study the problem of master-slave synchronization of two delayed memristive neural networks (MNNs). Different from most previous papers, memristors are regarded as uncertain continuous time-varying parameters, and MNNs are modeled by neural networks (NNs) with continuous time-varying parameters and polytopic uncertainty. Thus, synchronization of two delayed MNNs is converted into synchronization of delayed NNs with uncertain parameter mismatches. Quasi-synchronization criteria are derived by Lyapunov function and inequality technique. It is shown that, given a predetermined error bound, quasi-synchronization of two delayed chaotic MNNs can be achieved provided that the pinning strength is larger than a threshold. In the end, a numerical example is provided to illustrate the effectiveness of the derived results.

Event-Based Impulsive Control of Continuous-Time Dynamic Systems and Its Application to Synchronization of Memristive Neural Networks

This paper investigates exponential stabilization of continuous-time dynamic systems (CDSs) via event-based impulsive control (EIC) approaches, where the impulsive instants are determined by certain state-dependent triggering condition. The global exponential stability criteria via EIC are derived for nonlinear and linear CDSs, respectively. It is also shown that there is no Zeno-behavior for the concerned closed loop control system. In addition, the developed event-based impulsive scheme is applied to the synchronization problem of master and slave memristive neural networks. Furthermore, a self-triggered impulsive control scheme is developed to avoid continuous communication between the master system and slave system. Finally, two numerical simulation examples are presented to illustrate the effectiveness of the proposed event-based impulsive controllers.

Stability Analysis of Genetic Regulatory Networks With Switching Parameters and Time Delays

This paper is concerned with the exponential stability analysis of genetic regulatory networks (GRNs) with switching parameters and time delays. In this paper, a new integral inequality and an improved reciprocally convex combination inequality are considered. By using the average dwell time approach together with a novel Lyapunov-Krasovskii functional, we derived some conditions to ensure the switched GRNs with switching parameters and time delays are exponentially stable. Finally, we give two numerical examples to clarify that our derived results are effective.

Finite-Time Stabilization of Delayed Memristive Neural Networks: Discontinuous State-Feedback and Adaptive Control Approach

In this paper, a general class of delayed memristive neural networks (DMNNs) system described by functional differential equation with discontinuous right-hand side is considered. Under the extended Filippov-framework, we investigate the finite-time stabilization problem for DMNNs by using the famous finite-time stability theorem and the generalized Lyapunov functional method. To do so, we design two classes of novel controllers including discontinuous state-feedback controller and discontinuous adaptive controller. Without assuming the boundedness and monotonicity of the activation functions, several sufficient conditions are given to stabilize the states of this class of DMNNs in finite time. Moreover, the upper bounds of the settling time for stabilization are estimated. Finally, numerical examples are provided to demonstrate the effectiveness of the developed method and the theoretical results.

Delay-Dependent Global Exponential Stability for Delayed Recurrent Neural Networks

This paper deals with the global exponential stability for delayed recurrent neural networks (DRNNs). By constructing an augmented Lyapunov-Krasovskii functional and adopting the reciprocally convex combination approach and Wirtinger-based integral inequality, delay-dependent global exponential stability criteria are derived in terms of linear matrix inequalities. Meanwhile, a general and effective method on global exponential stability analysis for DRNNs is given through a lemma, where the exponential convergence rate can be estimated. With this lemma, some global asymptotic stability criteria of DRNNs acquired in previous studies can be generalized to global exponential stability ones. Finally, a frequently utilized numerical example is carried out to illustrate the effectiveness and merits of the proposed theoretical results.

Quantized Synchronization of Chaotic Neural Networks With Scheduled Output Feedback Control

In this paper, the synchronization problem of master-slave chaotic neural networks with remote sensors, quantization process, and communication time delays is investigated. The information communication channel between the master chaotic neural network and slave chaotic neural network consists of several remote sensors, with each sensor able to access only partial knowledge of output information of the master neural network. At each sampling instants, each sensor updates its own measurement and only one sensor is scheduled to transmit its latest information to the controller's side in order to update the control inputs for the slave neural network. Thus, such communication process and control strategy are much more energy-saving comparing with the traditional point-to-point scheme. Sufficient conditions for output feedback control gain matrix, allowable length of sampling intervals, and upper bound of network-induced delays are derived to ensure the quantized synchronization of master-slave chaotic neural networks. Lastly, Chua's circuit system and 4-D Hopfield neural network are simulated to validate the effectiveness of the main results.In this paper, the synchronization problem of master-slave chaotic neural networks with remote sensors, quantization process, and communication time delays is investigated. The information communication channel between the master chaotic neural network and slave chaotic neural network consists of several remote sensors, with each sensor able to access only partial knowledge of output information of the master neural network. At each sampling instants, each sensor updates its own measurement and only one sensor is scheduled to transmit its latest information to the controller's side in order to update the control inputs for the slave neural network. Thus, such communication process and control strategy are much more energy-saving comparing with the traditional point-to-point scheme. Sufficient conditions for output feedback control gain matrix, allowable length of sampling intervals, and upper bound of network-induced delays are derived to ensure the quantized synchronization of master-slave chaotic neural networks. Lastly, Chua's circuit system and 4-D Hopfield neural network are simulated to validate the effectiveness of the main results.

Neural Skyline Filtering for Imbalance Features Classification

In the current digitalized era, large datasets play a vital role in features extractions, information processing, knowledge mining and management. Sometimes, existing mining approaches are not sufficient to handle large volume of datasets. Biological data processing also suffers for the same issue. In the present work, a classification process is carried out on large volume of exons and introns from a set of raw data. The proposed work is designed into two parts as pre-processing and mapping-based classification. For pre-processing, three filtering techniques have been used. However, these traditional filtering techniques face difficulties for large datasets due to the long required time during large data processing as well as the large required memory size. In this regard, a mapping-based neural skyline filtering approach is designed. Randomized algorithm performed the mapping for large volume of datasets based on objective function. The objective function determines the randomized size of the datasets according to the homogeneity. Around 200 million DNA base pairs have been used for experimental analysis. Experimental result shows that mapping centric filtering outperforms other filtering techniques during large data processing.

Synchronization stability of memristor-based complex-valued neural networks with time delays

This paper focuses on the dynamical property of a class of memristor-based complex-valued neural networks (MCVNNs) with time delays. By constructing the appropriate Lyapunov functional and utilizing the inequality technique, sufficient conditions are proposed to guarantee exponential synchronization of the coupled systems based on drive-response concept. The proposed results are very easy to verify, and they also extend some previous related works on memristor-based real-valued neural networks. Meanwhile, the obtained sufficient conditions of this paper may be conducive to qualitative analysis of some complex-valued nonlinear delayed systems. A numerical example is given to demonstrate the effectiveness of our theoretical results.

Exponential Synchronization of Memristive Neural Networks With Delays: Interval Matrix Method

This paper considers the global exponential synchronization of drive-response memristive neural networks (MNNs) with heterogeneous time-varying delays. Because the parameters of MNNs are state-dependent, the MNNs may exhibit unexpected parameter mismatch when different initial conditions are chosen. Therefore, traditional robust control scheme cannot guarantee the synchronization of MNNs. Under the framework of Filippov solution, the drive and response MNNs are first transformed into systems with interval parameters. Then suitable controllers are designed to overcome the problem of mismatched parameters and synchronize the coupled MNNs. Based on some novel Lyapunov functionals and interval matrix inequalities, several sufficient conditions are derived to guarantee the exponential synchronization. Moreover, adaptive control is also investigated for the exponential synchronization. Numerical simulations are provided to illustrate the effectiveness of the theoretical analysis.

Event-Triggered State Estimation for Discrete-Time Multidelayed Neural Networks With Stochastic Parameters and Incomplete Measurements

In this paper, the event-triggered state estimation problem is investigated for a class of discrete-time multidelayed neural networks with stochastic parameters and incomplete measurements. In order to cater for more realistic transmission process of the neural signals, we make the first attempt to introduce a set of stochastic variables to characterize the random fluctuations of system parameters. In the addressed neural network model, the delays among the interconnections are allowed to be different, which are more general than those in the existing literature. The incomplete information under consideration includes randomly occurring sensor saturations and quantizations. For the purpose of energy saving, an event-triggered state estimator is constructed and a sufficient condition is given under which the estimation error dynamics is exponentially ultimately bounded in the mean square. It is worth noting that the ultimate boundedness of the error dynamics is explicitly estimated. The characterization of the desired estimator gain is designed in terms of the solution to a certain matrix inequality. Finally, a numerical simulation example is presented to illustrate the effectiveness of the proposed event-triggered state estimation scheme.

Exponential Stability of Complex-Valued Memristive Recurrent Neural Networks

In this brief, we establish a novel complex-valued memristive recurrent neural network (CVMRNN) to study its stability. As a generalization of real-valued memristive neural networks, CVMRNN can be separated into real and imaginary parts. By means of M -matrix and Lyapunov function, the existence, uniqueness, and exponential stability of the equilibrium point for CVMRNNs are investigated, and sufficient conditions are presented. Finally, the effectiveness of obtained results is illustrated by two numerical examples.

Impulsive Effects and Stability Analysis on Memristive Neural Networks With Variable Delays

In this brief, hybrid impulsive and adaptive feedback controllers are simultaneously exerted on a general delayed memristive neural network (MNN) model to formulate a novel impulsive controlled MNN (IMNN) model with variable delays. By means of Lyapunov-Razumikhin technique and other analytical ways, several new stability criteria of the proposed IMNN model are obtained. In addition, by choosing appropriate impulses and external inputs, the convergence speed of IMNN can be increased, which implies that its dynamic behaviors will be optimized. Finally, the effectiveness of the obtained results is illustrated by one numerical example.