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

Dynamic Event-Triggered Control for GSES of Memristive Neural Networks Under Multiple Cyber-Attacks

In this article, the dynamic event-triggered control problem of memristive neural networks (MNNs) under multiple cyber-attacks is considered. A novel dynamic event-triggering scheme (DETS) and the corresponding event-triggered controller are proposed by taking into consideration both denial-of-service and deception attacks (DoS-DAs). Then, a key lemma is established to show that the dynamic event-triggered controller can be used to solve the globally stochastically exponential stability (GSES) issue of concerned MNN under multiple cyber-attacks. Meanwhile, a novel Lyapunov functional is proposed based on the actual sampling pattern. It is shown that under our proposed dynamic event-triggered controller and Lyapunov functional, the concerned MNN can achieve GSES in the presence of DoS-DAs. In addition, our results include relevant results on event-triggered control of MNN with static event-triggering scheme (SETS) or without cyber-attacks as special cases. The effectiveness of the proposed event-triggered controller under multiple cyber-attacks is illustrated by a simulation example.

A hybrid trigger strategy based mixed impulsive control scheme on uncertain local field neural networks with leakage delay

Solved in this paper is the stabilization of uncertain local field neural networks (ULFNNs) with leakage delay by dint of a mixed impulsive control scheme. The impulsive control instants are decided by a Lyapunov functional-based event triggered scheme and a periodic impulse triggered scheme. Based on the proposed control scheme, sufficient conditions are deduced for eliminating the Zeno behavior and guaranteeing the uniform asymptotic stability (UAS) of the delayed ULFNNs in the framework of Lyapunov functional analysis method. Different from individual event triggered impulse control strategy where the triggered instants may be unexpected, the mixed impulsive control scheme can release the impulse control instants in line with the distance between any two adjacent successful control points, which improves the control performance and also achieves the goal of saving the communication resource. Furthermore, the decay behavior of impulse control signal is considered to make mathematical derivation more practical, and based on this behavior, a criterion is derived to make ensure the exponential stability of delayed ULFNNs. Finally, numerical examples are given to illustrate the effectiveness of the designed controller for the ULFNNs with leakage delay.

Impulsive strategies in nonlinear dynamical systems: A brief overview

The studies of impulsive dynamical systems have been thoroughly explored, and extensive publications have been made available. This study is mainly in the framework of continuous-time systems and aims to give an exhaustive review of several main kinds of impulsive strategies with different structures. Particularly, (i) two kinds of impulse-delay structures are discussed respectively according to the different parts where the time delay exists, and some potential effects of time delay in stability analysis are emphasized. (ii) The event-based impulsive control strategies are systematically introduced in the light of several novel event-triggered mechanisms determining the impulsive time sequences. (iii) The hybrid effects of impulses are emphatically stressed for nonlinear dynamical systems, and the constraint relationships between different impulses are revealed. (iv) The recent applications of impulses in the synchronization problem of dynamical networks are investigated. Based on the above several points, we make a detailed introduction for impulsive dynamical systems, and some significant stability results have been presented. Finally, several challenges are suggested for future works.

Improved Results on Fixed-/Preassigned-Time Synchronization for Memristive Complex-Valued Neural Networks

This article concerns the problems of synchronization in a fixed time or prespecified time for memristive complex-valued neural networks (MCVNNs), in which the state variables, activation functions, rates of neuron self-inhibition, neural connection memristive weights, and external inputs are all assumed to be complex-valued. First, the more comprehensive fixed-time stability theorem and more accurate estimations on settling time (ST) are systematically established by using the comparison principle. Second, by introducing different norms of complex numbers instead of decomposing the complex-valued system into real and imaginary parts, we successfully design several simpler discontinuous controllers to acquire much improved fixed-time synchronization (FXTS) results. Third, based on similar mathematical derivations, the preassigned-time synchronization (PATS) conditions are explored by newly developed new control strategies, in which ST can be prespecified and is independent of initial values and any parameters of neural networks and controllers. Finally, numerical simulations are provided to illustrate the effectiveness and superiority of the improved synchronization methodology.

Quasisynchronization of Memristive Neural Networks With Communication Delays via Event-Triggered Impulsive Control

This article considers the quasisynchronization of memristive neural networks (MNNs) with communication delays via event-triggered impulsive control (ETIC). In view of the limited communication and bandwidth, we adopt a novel switching event-triggered mechanism (ETM) that not only decreases the times of controller update and the amount of data sent out but also eliminates the Zeno behavior. By using an appropriate Lyapunov function, several algebraic conditions are given for quasisynchronization of MNNs with communication delays. More important, there is no restriction on the derivation of the Lyapunov function, even if it is an increasing function over a period of time. Then, we further propose a switching ETM depending on communication delays and aperiodic sampling, which is more economical and practical and can directly avoid Zeno behavior. Finally, two simulations are presented to validate the effectiveness of the proposed results.

A New Settling-time Estimation Protocol to Finite-time Synchronization of Impulsive Memristor-Based Neural Networks

In this article, the issues of finite-time synchronization and finite-time adaptive synchronization for the impulsive memristive neural networks (IMNNs) with discontinuous activation functions (DAFs) and hybrid impulsive effects are probed into and elaborated on, where the stabilizing impulses (SIs), inactive impulses (IIs), and destabilizing impulses (DIs) are taken into account, respectively. Not resembling several earlier works, a more extensive range of impulses in the context of impulsive effects has been analyzed without using the known average impulsive interval strategy (AIIS). In light of the theories of differential inclusions and set-valued map, as well as impulsive control, new sufficient criteria with respect to the estimated settling time for synchronization of the related IMNNs are established using two types of switching control approaches, which sufficiently utilize information from not only the SIs, DIs, and DAFs but also the impulse sequences. Two simulation experiments are presented to the efficiency of the proposed results.

Extended Robust Exponential Stability of Fuzzy Switched Memristive Inertial Neural Networks With Time-Varying Delays on Mode-Dependent Destabilizing Impulsive Control Protocol

This article investigates the problem of robust exponential stability of fuzzy switched memristive inertial neural networks (FSMINNs) with time-varying delays on mode-dependent destabilizing impulsive control protocol. The memristive model presented here is treated as a switched system rather than employing the theory of differential inclusion and set-value map. To optimize the robust exponentially stable process and reduce the cost of time, hybrid mode-dependent destabilizing impulsive and adaptive feedback controllers are simultaneously applied to stabilize FSMINNs. In the new model, the multiple impulsive effects exist between two switched modes, and the multiple switched effects may also occur between two impulsive instants. Based on switched analysis techniques, the Takagi-Sugeno (T-S) fuzzy method, and the average dwell time, extended robust exponential stability conditions are derived. Finally, simulation is provided to illustrate the effectiveness of the results.

Convolution Kernel Operations on a Two-Dimensional Spin Memristor Cross Array

In recent years, convolution operations often consume a lot of time and energy in deep learning algorithms, and convolution is usually used to remove noise or extract the edges of an image. However, under data-intensive conditions, frequent operations of the above algorithms will cause a significant memory/communication burden to the computing system. This paper proposes a circuit based on spin memristor cross array to solve the problems mentioned above. First, a logic switch based on spin memristors is proposed, which realizes the control of the memristor cross array. Secondly, a new type of spin memristor cross array and peripheral circuits is proposed, which realizes the multiplication and addition operation in the convolution operation and significantly alleviates the computational memory bottleneck. At last, the color image filtering and edge extraction simulation are carried out. By calculating the peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) of the image result, the processing effects of different operators are compared, and the correctness of the circuit is verified.

Exponential synchronization of stochastic delayed memristive neural networks via a novel hybrid control

This paper investigates the exponential synchronization issue of stochastic delayed memristive neural networks (SDMNNs) via a novel hybrid control (HC), where impulsive instants are determined by the state-dependent trigger condition. The switching and quantification strategies are applied to the event-based impulsive controller to cope with the challenges induced concurrently by interval parameters, impulses, stochastic disturbance and time-varying delays. Furthermore, the control costs can be reduced and communication channels and bandwidths can be saved by using this designed controller. Then, novel Lyapunov functions and new analytical methods are constructed, which can be used to realize the exponential synchronization of SDMNNs via HC. Finally, a numerical simulation is provided to demonstrate our theoretical results.

Impulsive Control of Nonlinear Systems With Time-Varying Delay and Applications

Impulsive control of nonlinear delay systems is studied in this paper, where the time delays addressed may be the constant delay, bounded time-varying delay, or unbounded time-varying delay. Based on the impulsive control theory and some analysis techniques, a new theoretical result for global exponential stability is derived from the impulsive control point of view. The significance of the presented result is that the stability can be achieved via the impulsive control at certain impulse points despite the existence of impulsive perturbations which causes negative effect to the control. That is, the impulsive control provides a super performance to allow the existence of impulsive perturbations. In addition, we apply the theoretical result to the problem of impulsive control of delayed neural networks. Some results for global exponential stability and synchronization control of neural networks with time delays are derived via impulsive control. Three illustrated examples are given to show the effectiveness and distinctiveness of the proposed impulsive control schemes.

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.

Multistability of Delayed Hybrid Impulsive Neural Networks With Application to Associative Memories

The important topic of multistability of continuous-and discrete-time neural network (NN) models has been investigated rather extensively. Concerning the design of associative memories, multistability of delayed hybrid NNs is studied in this paper with an emphasis on the impulse effects. Arising from the spiking phenomenon in biological networks, impulsive NNs provide an efficient model for synaptic interconnections among neurons. Using state-space decomposition, the coexistence of multiple equilibria of hybrid impulsive NNs is analyzed. Multistability criteria are then established regrading delayed hybrid impulsive neurodynamics, for which both the impulse effects on the convergence rate and the basins of attraction of the equilibria are discussed. Illustrative examples are given to verify the theoretical results and demonstrate an application to the design of associative memories. It is shown by an experimental example that delayed hybrid impulsive NNs have the advantages of high storage capacity and high fault tolerance when used for associative memories.

Stability of Singular Discrete-Time Neural Networks With State-Dependent Coefficients and Run-to-Run Control Strategies

In this brief, sustaining and intermittent run-to-run controllers are designed to achieve the stability of singular discrete-time neural networks with state-dependent coefficients. The controllers are designed for two reasons: 1) it is very difficult and almost impossible to only measure the in situ feedback information for the controllers and 2) the controllers may not always exist at any time. The stability is then established for singular discrete-time neural networks with state-dependent coefficients. Finally, numerical simulations are shown to illustrate the usefulness of the obtained criteria.

Dynamic Analysis of Hybrid Impulsive Delayed Neural Networks With Uncertainties

Neural networks (NNs) have emerged as a powerful illustrative diagram for the brain. Unveiling the mechanism of neural-dynamic evolution is one of the crucial steps toward understanding how the brain works and evolves. Inspired by the universal existence of impulses in many real systems, this paper formulates a type of hybrid NNs (HNNs) with impulses, time delays, and interval uncertainties, and studies its global dynamic evolution by a robust interval analysis. The HNNs incorporate both continuous-time implementation and impulsive jump in mutual activations, where time delays and interval uncertainties are represented simultaneously. By constructing a Banach contraction mapping, the existence and uniqueness of the equilibrium of the HNN model are proved and analyzed in detail. Based on nonsmooth Lyapunov functions and delayed impulsive differential equations, new criteria are derived for ensuring the global robust exponential stability of the HNNs. Convergence analysis together with illustrative examples show the effectiveness of the theoretical results.

Passivity analysis of memristor-based impulsive inertial neural networks with time-varying delays

This paper focuses on delay-dependent passivity analysis for a class of memristive impulsive inertial neural networks with time-varying delays. By choosing proper variable transformation, the memristive inertial neural networks can be rewritten as first-order differential equations. The memristive model presented here is regarded as a switching system rather than employing the theory of differential inclusion and set-value map. Based on matrix inequality and Lyapunov-Krasovskii functional method, several delay-dependent passivity conditions are obtained to ascertain the passivity of the addressed networks. In addition, the results obtained here contain those on the passivity for the addressed networks without impulse effects as special cases and can also be generalized to other neural networks with more complex pulse interference. Finally, one numerical example is presented to show the validity of the obtained results.

Route searching based on neural networks and heuristic reinforcement learning

In this paper, an improved and much stronger RNH-QL method based on RBF network and heuristic Q-learning was put forward for route searching in a larger state space. Firstly, it solves the problem of inefficiency of reinforcement learning if a given problem's state space is increased and there is a lack of prior information on the environment. Secondly, RBF network as weight updating rule, reward shaping can give an additional feedback to the agent in some intermediate states, which will help to guide the agent towards the goal state in a more controlled fashion. Meanwhile, with the process of Q-learning, it is accessible to the underlying dynamic knowledge, instead of the need of background knowledge of an upper level RBF network. Thirdly, it improves the learning efficiency by incorporating the greedy exploitation strategy to train the neural network, which has been testified by the experimental results.