Stochastic Memristive Neural Networks Research Articles

Global exponential stability and stabilization of stochastic memristive neural networks with spatial diffusions and hybrid delays

In this paper, the global exponential stability and stabilization problems are investigated for memristive neural networks (MNNs) with stochastic disturbances, spatial diffusions and distributed delays. The spatial diffusions are not assumed to be symmetric and distributed delays are relaxed to be unbounded. Then, the presented MNNs are modeled as a class of stochastic partial systems with hybrid delays. Based on nonsmooth analysis, the Lyapunov–Krasovskii functional and inequality approach, some simple algebraic criteria are derived for the global exponential stability as well as the stabilization via two kinds of designed feedback controllers. The derived criteria are easily verified and the obtained results are available for other delayed systems with or without stochastic disturbances and spatial diffusions. Finally, the stability and stabilization results are validated by numerical simulations.

Synchronization of stochastic memristive neural networks via event‐triggered impulsive control

AbstractThis paper investigates the synchronization problem for master‐slave stochastic memristive neural networks (SMNNs) with time‐delay via event‐triggered impulsive control (ETIC). Firstly, a novel ETIC method is designed for SMNNs to realize quasi‐synchronization in mean square sense. Different from time‐triggered impulsive control (TTIC) in the existing results on SMNNs, the proposed event‐triggered method determines impulsive instants based on the real‐time system states, which can reduce redundant impulses. Compared with the existing ETIC for deterministic memristive neural networks (MNNs), the proposed event‐triggered mechanism (ETM) can exclude Zeno behavior completely by adding the waiting time, when stochastic disturbances occur in MNNs. Secondly, if the master SMNNs have nonzero control inputs, an adaptive‐impulsive hybrid controller with ETM is designed to realize almost surely exponential synchronization. Under the ETM, the number of transmitted events is reduced, then control resources can be saved. Zeno behavior can be excluded in almost sure sense. Ultimately, simulations are presented to illustrate the validity of the obtained results.

Finite-Time Synchronization for Stochastic Fractional-Order Memristive BAM Neural Networks with Multiple Delays

This paper studies the finite-time synchronization problem of fractional-order stochastic memristive bidirectional associative memory neural networks (MBAMNNs) with discontinuous jumps. A novel criterion for finite-time synchronization is obtained by utilizing the properties of quadratic fractional-order Gronwall inequality with time delay and the comparison principle. This criterion provides a new approach to analyze the finite-time synchronization problem of neural networks with stochasticity. Finally, numerical simulations are provided to demonstrate the effectiveness and superiority of the obtained results.

Pinning synchronization of stochastic neutral memristive neural networks with reaction–diffusion terms

This paper investigates the pinning synchronization of stochastic neutral memristive neural networks with reaction–diffusion terms. Firstly, two novel pinning controllers, which contain both current state and past state, are designed. Subsequently, in terms of Green’s theorem, inequality technology, stochastic analysis theory and pinning control technology, two easy-to-test sufficient conditions based on algebraic inequalities are obtained to ensure the mean-square asymptotic synchronization of stochastic memristive neural networks with neutral delays and reaction–diffusion terms by providing a new Lyapunov–Krasovskii functional. In addition, some existing results can be regarded as special cases of our work. Finally, illustrative examples further verify the correctness and validity of the derived results.

Quasi-synchronization of stochastic memristive neural networks subject to deception attacks

Quasi-synchronization of stochastic memristive neural networks subject to deception attacks

Synchronization of Stochastic Memristive Neural Networks with Retarded and Advanced Argument

In this paper, we discuss the driving-response synchronization problem for two memristive neural networks with retarded and advanced arguments under the condition of additional noise. The control law is related to the linear time-delay feedback term, and the discontinuous feedback term. Moreover, the random different equation is used to prove the stability of this theory. At the end, the simulation results verify the correctness of the theoretical results.

Synchronization Analysis for Stochastic Inertial Memristor-Based Neural Networks with Linear Coupling

This paper concerns the synchronization problem for a class of stochastic memristive neural networks with inertial term, linear coupling, and time-varying delay. Based on the interval parametric uncertainty theory, the stochastic inertial memristor-based neural networks (IMNNs for short) with linear coupling are transformed to a stochastic interval parametric uncertain system. Furthermore, by applying the Lyapunov stability theorem, the stochastic analysis approach, and the Halanay inequality, some sufficient conditions are obtained to realize synchronization in mean square. The established criteria show that stochastic perturbation is designed to ensure that the coupled IMNNs can be synchronized better by changing the state coefficients of stochastic perturbation. Finally, an illustrative example is presented to demonstrate the efficiency of the theoretical results.

Almost sure exponential synchronization of drive-response stochastic memristive neural networks

Abstract This paper concerns with the almost sure exponential synchronization for some general classes of drive-response stochastic memristive neural networks (SMNNs) with nonidentical nodes under state feedback controllers. The SMNNs considered may include networks which are asymmetrically nondelayed and delayed coupled simultaneously, and state-dependent or even those that are subject to exogenous stochastic perturbations representatively. The main results of this paper are a collection of generic sufficient conditions for guaranteed almost sure exponential synchronization of these SMNNs, which performs great advantages compared with mean-square synchronization. Furthermore, some practical corollaries are also obtained from the main results that may be directly applied to some smaller subclasses of these networks. In particular, a simpler and more effective way of almost surely exponentially synchronizing SMNNs without delays follows by considering them as a special case of SMNNs with delays. Some numerical simulations are given to illustrate our main theoretical findings.

Stochastic Memristive Quaternion-Valued Neural Networks with Time Delays: An Analysis on Mean Square Exponential Input-to-State Stability

In this paper, we study the mean-square exponential input-to-state stability (exp-ISS) problem for a new class of neural network (NN) models, i.e., continuous-time stochastic memristive quaternion-valued neural networks (SMQVNNs) with time delays. Firstly, in order to overcome the difficulties posed by non-commutative quaternion multiplication, we decompose the original SMQVNNs into four real-valued models. Secondly, by constructing suitable Lyapunov functional and applying It o ^ ’s formula, Dynkin’s formula as well as inequity techniques, we prove that the considered system model is mean-square exp-ISS. In comparison with the conventional research on stability, we derive a new mean-square exp-ISS criterion for SMQVNNs. The results obtained in this paper are the general case of previously known results in complex and real fields. Finally, a numerical example has been provided to show the effectiveness of the obtained theoretical results.

Mean-square Stability in Lagrange Sense for Stochastic Memristive Neural Networks with Leakage Delay

In this paper, a class of stochastic memristive neural networks with leakage delay, discrete and distribute transmission delays is investigated. Based on the theory of Filippov’s solution, by using Lyapunov-Krasovskii functionals, the free-weighting matrix method and stochastic analysis technique, a sufficient criterion in terms of linear matrix inequalities (LMIs) is given to ascertain the network to be exponentially Lagrange stable in mean square sense, which can be easily checked via MATLAB. Meanwhile the estimation of globally attractive set is given. Finally, numerical simulations are carried out to illustrate the feasibility of theoretical results.

Exponential Synchronization of Stochastic Memristive Neural Networks with Time-Varying Delays

This paper pays attention to the synchronization control methodology for stochastic memristive system. On the framework of Lyapunov functional, stability theory and free-weighting matrices technique, some brand-new solvability criteria are established to ensure the exponential synchronization goal of the target model. Considering the introduce of some free-weighting matrices, the obtained synchronization verdict will be much more applicable. Finally, the living example is included to show the effectiveness of the presented methodology.

Exponential Synchronization of Stochastic Memristive Recurrent Neural Networks Under Alternate State Feedback Control

This paper solves the exponential synchronization problem of two memristive recurrent neural networks with both stochastic disturbance and time-varying delays via periodically alternate state feedback control. First, a periodically alternate state feedback control rule is designed. Then, on the basis of the Lyapunov stability theory, some novel sufficient conditions guaranteeing exponential synchronization of drive-response stochastic memristive recurrent neural networks via periodically alternate state feedback control are derived. In contrast to some previous works about synchronization of memristive recurrent neural networks, the obtained results in this paper are not difficult to be validated, and complement, extend and generalize the earlier papers. Lastly, an illustrative example is provided to indicate the effectiveness and applicability of the obtained theoretical results.

Stability analysis for discrete-time stochastic memristive neural networks with both leakage and probabilistic delays

This paper is concerned with the globally exponential stability problem for a class of discrete-time stochastic memristive neural networks (DSMNNs) with both leakage delays as well as probabilistic time-varying delays. For the probabilistic delays, a sequence of Bernoulli distributed random variables is utilized to determine within which intervals the time-varying delays fall at certain time instant. The sector-bounded activation function is considered in the addressed DSMNN. By taking into account the state-dependent characteristics of the network parameters and choosing an appropriate Lyapunov–Krasovskii functional, some sufficient conditions are established under which the underlying DSMNN is globally exponentially stable in the mean square. The derived conditions are made dependent on both the leakage and the probabilistic delays, and are therefore less conservative than the traditional delay-independent criteria. A simulation example is given to show the effectiveness of the proposed stability criterion.

$$H_{\infty }$$ H ∞ state estimation for discrete-time stochastic memristive BAM neural networks with mixed time-delays

In this paper, the $$H_\infty$$ state estimation problem is investigated for a class of discrete-time stochastic memristive bidirectional associative memory (DSMBAM) neural networks with mixed time delays. The mixed time delays comprise both discrete and distributed time-delays. A series of novel switching functions are proposed to reflect the state-dependent characteristics of the memristive connection weights in the discrete-time setting, which facilitates the dynamics analysis of the addressed memristive neural networks (MNNs). By means of the introduced series of switching functions, an $$H_\infty$$ state estimator is designed such that the estimation error is exponentially mean-square stable and the prescribed $$H_\infty$$ performance requirement is achieved. The gain matrices of the desired estimator are parameterized by utilizing the semi-definite programming method. Finally, a simulation example is employed to demonstrate the usefulness and effectiveness of the proposed theoretical results.

Exponential stabilisation of stochastic memristive neural networks under intermittent adaptive control

This study focuses on the exponential stabilisation problem for a general class of memristive neural networks subjected to both stochastic disturbance and time-varying delays under periodically intermittent adaptive control. The stochastic disturbances are described as Brownian motions in the considered networks. An adaptive updated rule and a periodically intermittent adaptive control strategy are designed for the exponential stabilisation of memristive neural networks subjected to both stochastic disturbance and time-varying delays. Then, by adopting the adaptive control technique, differential inclusion theory and set-valued maps, and by building a new Lyapunov–Krasovskii functional, many novel sufficient conditions are proposed to guarantee exponential stabilisation for stochastic memristive neural networks. Different from existing results on stabilisation of stochastic memristive neural networks, the obtained criteria in this study are directly derived according to the parameters of networks. Finally, an example is carried out to demonstrate the validity of the theoretic results.

Event-Triggered State Estimation for Delayed Stochastic Memristive Neural Networks With Missing Measurements: The Discrete Time Case.

In this paper, the event-triggered state estimation problem is investigated for a class of discrete-time stochastic memristive neural networks (DSMNNs) with time-varying delays and missing measurements. The DSMNN is subject to both the additive deterministic disturbances and the multiplicative stochastic noises. The missing measurements are governed by a sequence of random variables obeying the Bernoulli distribution. For the purpose of energy saving, an event-triggered communication scheme is used for DSMNNs to determine whether the measurement output is transmitted to the estimator or not. The problem addressed is to design an event-triggered estimator such that the dynamics of the estimation error is exponentially mean-square stable and the prespecified disturbance rejection attenuation level is also guaranteed. By utilizing a Lyapunov-Krasovskii functional and stochastic analysis techniques, sufficient conditions are derived to guarantee the existence of the desired estimator, and then, the estimator gains are characterized in terms of the solution to certain matrix inequalities. Finally, a numerical example is used to demonstrate the usefulness of the proposed event-triggered state estimation scheme.

Exponential adaptive synchronization of stochastic memristive chaotic recurrent neural networks with time-varying delays

This paper is focused on the global exponential adaptive synchronization problem of two stochastic memristive chaotic neural networks with both stochastic disturbance and time-varying delays. First, in order to develop the guaranteed cost control, a periodically alternate adaptive rule is designed. Then, by constructing appropriate Lyapunov–Krasovskii functionals, several easily verified synchronization criteria are derived to guarantee exponential adaptive synchronization of drive-response stochastic memristive chaotic recurrent neural networks. Lastly, a numerical simulation is carried out to demonstrate the effectiveness of the proposed results.

Mean square exponential input-to-state stability of stochastic memristive complex-valued neural networks with time varying delay

ABSTRACTIn this paper, mean square exponential input-to-state stability (exp-ISS) of stochastic memristive complex-valued neural networks (SMCVNNs) is investigated. By utilising Lyapunov functional and stochastic analysis theory, a sufficient criterion is derived to assure the mean square exp-ISS of the SMCVNNs. The obtained results not only generalise the previous works in the literature about real-valued neural networks as special cases, but also can be easily checked by parameters of system. Numerical simulations are given to show the effectiveness of our theoretical results.

Stability Analysis for Stochastic Neutral-Type Memristive Neural Networks with Time-Varying Delay and S-Type Distributed Delays

In this paper, we consider the input-to-stability for a class of stochastic neutral-type memristive neural networks. Neutral terms and S-type distributed delays are taken into account in our system. Using the stochastic analysis theory and Itô formula, we obtain the conditions of mean-square exponential input-to-stability for system. A numerical example is given to illustrate the correctness of our conclusions.

Exponential Antisynchronization Control of Stochastic Memristive Neural Networks with Mixed Time-Varying Delays Based on Novel Delay-Dependent or Delay-Independent Adaptive Controller

The global exponential antisynchronization in mean square of memristive neural networks with stochastic perturbation and mixed time-varying delays is studied in this paper. Then, two kinds of novel delay-dependent and delay-independent adaptive controllers are designed. With the ability of adapting to environment changes, the proposed controllers can modify their behaviors to achieve the best performance. In particular, on the basis of the differential inclusions theory, inequality theory, and stochastic analysis techniques, several sufficient conditions are obtained to guarantee the exponential antisynchronization between the drive system and response system. Furthermore, two numerical simulation examples are provided to the validity of the derived criteria.