Stochastic stability of delayed neural networks with local impulsive effects

Exponential synchronization of delayed coupled neural networks with delay-compensatory impulsive control

This paper studies the exponential synchronization problem for a class of delayed coupled neural networks with delay-compensatory impulsive control. A Razumikhin-type inequality involving some destabilizing delayed impulse gains and a new idea of delay-compensatory that shows two critical roles for system stability are presented, respectively. Based on the constructed inequality and the presented delay-compensatory idea, sufficient stability and synchronization criteria for globally exponential synchronization (GES) of coupled neural networks (CNNs) are presented. Compared with existing results, the uniqueness of the presented results lies in that impulse delays can be fetched and integrated to compensate for instantaneous unstable impulse dynamics caused by destabilizing gains. Moreover, constraints between system delay and impulsive delay are relaxed, and the interval of impulses no longer constrains the system delay. Comparisons and a practical application are given to demonstrate the superior performance of the presented novel control methods.

Robust exponential stability of discrete-time uncertain impulsive stochastic neural networks with delayed impulses

This paper is devoted to the study of the robust exponential stability (RES) of discrete-time uncertain impulsive stochastic neural networks (DTUISNNs) with delayed impulses. Using Lyapunov function methods and Razumikhin techniques, a number of sufficient conditions for mean square (RES-ms) robust exponential stability are derived. The obtained results show that the hybrid dynamic is RES-ms with regard to lower boundary of impulse interval if the discrete-time stochastic neural networks (DTSNNs) is RES-ms and that the impulsive effects are instable. Conversely, if DTSNNs is not RES-ms, impulsive effects can induce unstable neural networks (NNs) to stabilize again concerning an upper bound of the impulsive interval. The results obtained in this study have a broader scope of application than some previously existing findings. Two numerical examples were presented to verify the availability and advantages of the results.

Constrained hybrid control for parametric uncertainty systems via step-function method

In this paper, considering that sometimes signal transmission may be interrupted, or signal input errors may occur, we establish a novel class of parametric uncertainty hybrid control system models including the impulsive control signals under saturated inputs, which can reflect the signal transmission process more realistically. Based on the step-function method, improved polytopic representation approach and Schur complement, we find the stability conditions, which are less conservative than those with the traditional Lyapunov method, of the considered control system. In addition, we investigate the design of the control gains and the auxiliary control gains for easily finding the suitable control signals, the auxiliary signals and the estimation of the attraction domain. Moreover, our proposed methods are applied to the fixed time impulse problems of uncertain systems with or without Zeno behavior. Simulation results for the uncertain neural network systems are presented to show the feasibility and effectiveness of our stabilization methods using the step-function.

Event-Triggered Exponential Synchronization for Complex-Valued Memristive Neural Networks With Time-Varying Delays

This article solves the event-triggered exponential synchronization problem for a class of complex-valued memristive neural networks with time-varying delays. The drive-response complex-valued memristive neural networks are translated into two real-valued memristive neural networks through the method of separating the complex-valued memristive neural networks into real and imaginary parts. In order to reduce the information exchange frequency between the sensor and the controller, a novel event-triggered mechanism with the event-triggering functions is introduced in wireless communication networks. Some sufficient conditions are established to achieve the event-triggered exponential synchronization for drive-response complex-valued memristive neural networks with time-varying delays. In addition, to guarantee that the Zeno behavior cannot occur, a positive lower bound for the interevent times is explicitly derived. Finally, numerical simulations are provided to illustrate the effectiveness and superiority of the obtained theoretical results.

Delay-Distribution-Dependent H∞ State Estimation for Discrete-Time Memristive Neural Networks With Mixed Time-Delays and Fading Measurements

This paper addresses the H _∞ state estimation issue for a sort of memristive neural networks in the discrete-time setting under randomly occurring mixed time-delays and fading measurements. The main purpose of the addressed issue is to propose a state estimator design algorithm that ensures the error dynamics of the state estimation to be stochastically stable with a prespecified H _∞ disturbance attenuation index. We put forward certain switching functions to account for the discrete-time yet state-dependent characteristics of the memristive connection weights. By resorting to the robust analysis theory and the Lyapunov-functional analysis theory, we derive some sufficient conditions to guarantee the desired estimation performance. The derived sufficient conditions rely not only on the size of discrete time-delays and the probability distribution law of the distributed time-delays but also on the statistics information of the coefficients of the adopted Rice fading model. Based on the established existence conditions, the gain matrices of the desired estimator are obtained by means of the feasibility of a set of matrix inequalities that can be checked efficiently via available software packages. Finally, the numerical simulation results are provided to show the validity of the main results.

Generative dynamic link prediction

In networks, a link prediction task aims at learning potential relations between nodes to predict unknown potential linkage states. At present, most link prediction methods are used to process static networks. These methods cannot produce good prediction results for dynamic networks. However, for most dynamic networks in the real world, the vertices and links of these networks change over time. Dynamic link prediction (DLP) has attracted more attention as it can better mimic the evolution nature of the networks. Inspired by successful applications of the generative adversarial network in generating fake images, which are comparable with the real ones, we propose a novel generative dynamic link prediction (GDLP) method. Different from other DLP methods, we model the link prediction task as a network generation process. More specifically, GDLP utilizes the historical networks structure information to generate the network snapshot of next time stamp by an end-to-end deep generative model. This model contains a generator and a discriminator. The generator of GDLP is a spatiotemporal prediction model, which is responsible for generating the future networks based on the historical network snapshots, while the discriminator is a classification model to classify the generated networks and the ground-truth ones. With the two-player game training and learning strategy, GDLP is capable of accurate prediction for dynamic networks using the structural and temporal information. Experimental results validate that GDLP significantly outperforms several existing baseline methods on many types of dynamic networks, which improves the effectiveness of dynamic link prediction.

Reduced- and Full-Order Observers for Delayed Genetic Regulatory Networks

This paper is centered upon the state estimation for delayed genetic regulatory networks. Our aim is at estimating the concentrations of mRNAs and proteins by designing reduced-order and full-order state observers based on available network outputs. We introduce a Lyapunov-Krasovskii functional including quadruplicate integrals, and estimate its derivative by employing the Wirtinger-type integral inequalities, reciprocal convex technique, and convex technique. From which, delay-dependent sufficient conditions, in the form of linear matrix inequalities (LMIs), are investigated to ensure that the resultant error system is asymptotically stable. One can verify these conditions by utilizing the MATLAB Toolboxes LMI or YALMIP. In addition, the gains of reduced-order and full-order observers are represented by the feasible solutions of the LMIs, and thereby, the concrete expressions of the desired reduced-order and full-order state observers are presented. Finally, the simulation results of a numerical example are demonstrated, which explains the validity of the proposed method.

Stability Analysis and Application for Delayed Neural Networks Driven by Fractional Brownian Noise

This paper deals with two types of the stability problem for the delayed neural networks driven by fractional Brownian noise (FBN). The existence and the uniqueness of the solution to the main system with respect to FBN are proved via fixed point theory. Based on Hilbert-Schmidt operator theory and analytic semigroup principle, the mild solution of the stochastic neural networks is obtained. By applying the stochastic analytic technique and some well-known inequalities, the asymptotic stability criteria and the exponential stability condition are established. Both numerical example and practical application for synchronization control of multiagent system are provided to illustrate the effectiveness and potential of the proposed techniques.

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.

Stability analysis of hybrid neural networks with impulsive time window

The urgent problem with impulsive moments cannot be determined in advance brings new challenges beyond the conventional impulsive systems theory. In order to solve this problem, in this paper, a novel class of system with impulsive time window is proposed. Different from the conventional impulsive control strategies, the main characteristic of the impulsive time window is that impulse occurs in a random manner. Moreover, for the importance of the hybrid neural networks, using switching Lyapunov functions and a generalized Hanlanay inequality, some general criteria for asymptotic and exponential stability of the hybrid neural networks with impulsive time window are established. Finally, some simulations are provided to further illustrate the effectiveness of the results.