Stochastic Bidirectional Associative Memory Research Articles

Synchronization of Takagi–Sugeno Fuzzy Time-Delayed Stochastic Bidirectional Associative Memory Neural Networks Driven by Brownian Motion in Pre-Assigned Settling Time

We are devoted, in this paper, to the study of the pre-assigned-time drive-response synchronization problem for a class of Takagi–Sugeno fuzzy logic-based stochastic bidirectional associative memory neural networks, driven by Brownian motion, with continuous-time delay and (finitely and infinitely) distributed time delay. To achieve the drive-response synchronization between the neural network systems, concerned in this paper, and the corresponding response neural network systems (identical to our concerned neural network systems), we bring forward, based on the structural properties, a class of control strategies. By meticulously coining an elaborate Lyapunov–Krasovskii functional, we prove a criterion guaranteeing the desired pre-assigned-time drive-response synchronizability: For any given positive time instant, some of our designed controls make sure that our concerned neural network systems and the corresponding response neural network systems achieve synchronization, with the settling times not exceeding the pre-assigned positive time instant. In addition, we equip our theoretical studies with a numerical example, to illustrate that the synchronization controls designed in this paper are indeed effective. Our concerned neural network systems incorporate several types of time delays simultaneously, in particular, they have a continuous-time delay in their leakage terms, are based on Takagi–Sugeno fuzzy logic, and can be synchronized before any pre-given finite-time instant by the suggested control; therefore, our theoretical results in this paper have wide potential applications in the real world. The conservatism is reduced by introducing parameters in our designed Lyapunov–Krasovskii functional and synchronization control.

Impulsive effects on stochastic bidirectional associative memory neural networks with reaction-diffusion and leakage delays

In this paper, the problem of global asymptotic stability analysis for stochastic reaction-diffusion bidirectional associative memory neural networks (BAMNNs) with mixed delays and impulsive effects are investigated. The mixed delays consists of time delays in the leakage terms and continuously distributed delays. Based on the Lyapunov–Krasovskii functional (LKF), It's differential formula and linear matrix inequality (LMI) method, some sufficient conditions for global asymptotic stability in mean square of the equilibrium point of the systems are derived. The feasibility of the conditions are verified using the MATLAB LMI toolbox. Finally, two examples are provided to illustrate the effectiveness and validity of the derived main results.

Further mean-square asymptotic stability of impulsive discrete-time stochastic BAM neural networks with Markovian jumping and multiple time-varying delays

In this paper, the asymptotic stability analysis is investigated for a kind of discrete-time bidirectional associative memory (BAM) neural networks with the existence of perturbations namely, stochastic, Markovian jumping and impulses. Based on the theory of stability, a novel Lyapunov–Krasovskii function is constructed and by utilizing the concept of delay partitioning approach, a new linear-matrix-inequality (LMI) based criterion for the stability of such a system is proposed. Furthermore, the derived sufficient conditions are expressed in the structure of LMI, which can be easily verified by a known software package that guarantees the globally asymptotic stability of the equilibrium point. Eventually, a numerical example with simulation is given to demonstrate the effectiveness and applicability of the proposed method.

Mean-square exponential stability of fuzzy stochastic BAM networks with hybrid delays

We study fuzzy stochastic bidirectional associative memory cellular neural networks with discrete delays in leakage terms and with continuous and infinitely distributed delays in the transmission terms. Under certain structural assumptions, we prove that the networks in question are mean-square exponentially stable. Our main ingredient is the classical direct Lyapunov approach, in which we construct an elaborate Lyapunov–Krasovskii function. The arguments in the paper can be readily adapted to study stability problems for other cellular neural networks.

Global exponential stability of antiperiodic solutions for impulsive discrete‐time Markovian jumping stochastic BAM neural networks with additive time‐varying delays and leakage delay

SummaryThis paper presents a global exponential stability of antiperiodic solution for a class of impulsive discrete‐time Markovian jumping stochastic bidirectional associative memory neural networks with additive time‐varying delays and leakage delay. By utilizing the Lyapunov‐Krasovskii functional and contraction mapping principle, several sufficient conditions and linear matrix inequalities are derived for verifying globally exponentially stable in the mean square. There is a new delay‐dependent criterion for checking the existence, uniqueness, and global stability for antiperiodic solution. Meantime, by using the numerically efficient MATLAB Toolbox, simulation examples are offered to show the effectiveness and usefulness of the obtained result.

Synchronization of a Class of Memristive Stochastic Bidirectional Associative Memory Neural Networks with Mixed Time-Varying Delays via Sampled-Data Control

The paper addresses the issue of synchronization of memristive bidirectional associative memory neural networks (MBAMNNs) with mixed time-varying delays and stochastic perturbation via a sampled-data controller. First, we propose a new model of MBAMNNs with mixed time-varying delays. In the proposed approach, the mixed delays include time-varying distributed delays and discrete delays. Second, we design a new method of sampled-data control for the stochastic MBAMNNs. Traditional control methods lack the capability of reflecting variable synaptic weights. In this paper, the methods are carefully designed to confirm the synchronization processes are suitable for the feather of the memristor. Third, sufficient criteria guaranteeing the synchronization of the systems are derived based on the derive-response concept. Finally, the effectiveness of the proposed mechanism is validated with numerical experiments.

Formula omitted]th moment exponential stability of stochastic memristor-based bidirectional associative memory (BAM) neural networks with time delays

Stochastic memristor-based bidirectional associative memory (BAM) neural networks with time delays play an increasingly important role in the design and implementation of neural network systems. Under the framework of Filippov solutions, the issues of the pth moment exponential stability of stochastic memristor-based BAM neural networks are investigated. By using the stochastic stability theory, Itô’s differential formula and Young inequality, the criteria are derived. Meanwhile, with Lyapunov approach and Cauchy–Schwarz inequality, we derive some sufficient conditions for the mean square exponential stability of the above systems. The obtained results improve and extend previous works on memristor-based or usual neural networks dynamical systems. Four numerical examples are provided to illustrate the effectiveness of the proposed results.

A graph-theoretic approach to exponential stability of stochastic BAM neural networks with time-varying delays

This paper investigates the global exponential stability for a stochastic bidirectional associative memory (BAM) neural network with time-varying delays. Based on the principle of graph theory, a new method for pth moment exponential stability is derived by combining some inequalities, Lyapunov method and stochastic analysis. The obtained criteria have close relations to the topology property of the BAM neural network. Finally, a numerical example is provided to demonstrate the effectiveness and applicability of the theoretical results.

New passivity criteria for memristor-based neutral-type stochastic BAM neural networks with mixed time-varying delays

This paper deals with the problem of passivity analysis issue for a class of memristor-based neutral-type stochastic bidirectional associative memory neural networks (MNSBAMNNs) with discrete interval and distributed time-varying delays. By constructing new Lyapunov–Krasovskii functional (LKF) with quadruple integral terms and suitable activation function conditions, some delay-dependent passivity criteria are obtained in the linear matrix inequality (LMI) format. A numerical example is given to demonstrate the effectiveness and superiority of the new scheme.

Mean square stabilization and mean square exponential stabilization of stochastic BAM neural networks with Markovian jumping parameters

This paper addresses the mean square exponential stabilization problem of stochastic bidirectional associative memory (BAM) neural networks with Markovian jumping parameters and time-varying delays. By establishing a proper Lyapunov–Krasovskii functional and combining with LMIs technique, several sufficient conditions are derived for ensuring exponential stabilization in the mean square sense of such stochastic BAM neural networks. In addition, the achieved results are not difficult to verify for determining the mean square exponential stabilization of delayed BAM neural networks with Markovian jumping parameters and impose less restrictive and less conservative than the ones in previous papers. Finally, numerical results are given to show the effectiveness and applicability of the achieved results.

Stability of stochastic fuzzy BAM neural networks with discrete and distributed time-varying delays

Among the various fuzzy models, the well-known Takagi–Sugeno (T–S) fuzzy model is recognized as a popular and powerful tool in approximating a complex nonlinear system. T–S model provides a fixed structure to some nonlinear systems and facilitates the analysis of the system. This paper deals with the global stability of stochastic bidirectional associative memory (BAM) neural networks with discrete and distributed time-varying delays which are represented by the T–S fuzzy models. The stability conditions are derived using Lyapunov–Krasovskii functional combined with the linear matrix inequality (LMI) techniques. Finally, numerical examples are given to demonstrate the correctness of the theoretical results.

Robust Exponential Stability of Stochastic Discrete-Time BAM Neural Networks with Markovian Jumping Parameters and Delays

The problem of robustly globally exponential stability in the mean square is investigated for stochastic uncertain discrete-time bidirectional associative memory (BAM) neural networks with time-varying delays and Markovian jumping parameters. The uncertainties are assumed to be the linear fractional form. By using Lyapunov-Krasovskii functional (LKF) method and some novel technique, a delay-dependent exponential stability criterion is established in terms of linear matrix inequalities (LMIs). A numerical example is provided to show the effectiveness and the improvement of the proposed methods.

Exponential stability for markovian jumping stochastic BAM neural networks with mode‐dependent probabilistic time‐varying delays and impulse control

In this article, an exponential stability analysis of Markovian jumping stochastic bidirectional associative memory (BAM) neural networks with mode‐dependent probabilistic time‐varying delays and impulsive control is investigated. By establishment of a stochastic variable with Bernoulli distribution, the information of probabilistic time‐varying delay is considered and transformed into one with deterministic time‐varying delay and stochastic parameters. By fully taking the inherent characteristic of such kind of stochastic BAM neural networks into account, a novel Lyapunov‐Krasovskii functional is constructed with as many as possible positive definite matrices which depends on the system mode and a triple‐integral term is introduced for deriving the delay‐dependent stability conditions. Furthermore, mode‐dependent mean square exponential stability criteria are derived by constructing a new Lyapunov‐Krasovskii functional with modes in the integral terms and using some stochastic analysis techniques. The criteria are formulated in terms of a set of linear matrix inequalities, which can be checked efficiently by use of some standard numerical packages. Finally, numerical examples and its simulations are given to demonstrate the usefulness and effectiveness of the proposed results. © 2014 Wiley Periodicals, Inc. Complexity 20: 39–65, 2015

Passivity analysis for uncertain discrete-time stochastic BAM neural networks with time-varying delays

This paper is concerned with the passivity analysis problem for a class of discrete-time stochastic bidirectional associative memory neural networks with time-varying delays. Furthermore, the results are extended to the robust passivity analysis with mixed time delays that consist of both the discrete and distributed time delays, and the uncertainties are assumed to be time-varying norm bounded parameter uncertainties. By constructing a new Lyapunov---Krasovskii functional and introducing some appropriate free-weighting matrices, a delay-dependent passivity criterion is derived in terms of LMIs whose feasibility can be easily checked by some available software packages. Finally, two numerical examples with simulation results are given to demonstrate the effectiveness and usefulness of the proposed results.

Advances in neural network based learning

In recent years, the applications of diverse machine leaning algorithms and their fusion to the cybernetics and decisionmaking have been attracting more and more scholars from different disciplines. As a most frequently used technique of extracting knowledge from data, a feed-forwarded neural network (NN) has shown more advantages for the regression and classification problems. The main advantages come from the capability of good approximation of NNs and their corresponding highly nonlinear boundary. Due to the many merits and wide applications of NNs, the study on several fundamental issues of NNs, such as structure selection, overtraining, robustness and capability of resistance to noisy data, training on different types of data, and more importantly, the generalization ability, are still in progress although NNs have been an old topic in the areas of learning and reasoning. As a result, these extensive studies and significant improvements bring a number of new features anddevelopments to NNs. This issue makes an attempt to provide some latest advances of NN learning, the recent improvements of performance for NN learning systems, and new applications of NNs to different real fields. In this issue, 14 papers are accepted for publication. The 14 papers cover a variety of topics which include the stochastic stability NN with time delay, imbalanced and uncertain data, fuzzy NNs, bidirectional associative memory (BAM), deep learning of NNs, and other comparative and review studies. Categorization and brief description of these papers are given below. Four papers discuss the stability of NNs with delay time. Actually, the time delay is ubiquitous in most natural systems. Since the time delay is frequently encountered in NNs, the issue about stability of NNs with delay has been emerging as a challenging task for NN researchers. The paper authored by Cheng-De Zheng studied a class of stochastic reaction diffusion NNs with Markovian jumping parameters and time delays. Lyapunov functional method and stochastic analysis technique are used there to construct a new stochastic stability in the principle of the mean square. Continuing this topic, the paper authored by M. Syed Ali studied the stochastic stability analysis of uncertain recurrent NNs, also with Markovian jumping parameters and time varying delays. By using Lyapunov functional theory, Ito differential rule and matrix analysis techniques, a sufficient criterion in term of linear matrix inequality (LMI) is established such that, for all admissible parameter uncertainties and stochastic disturbances, the stochastic NN is perfectly stable. And then, a non-stationary problem on BAM NNs is discussed in Qingqing He’s paper. An exponential stability in terms of LMIs is achieved for a class of interval C-G type (BAM) NNs with the mixed time delays and non-smooth behaved functions by using Homomorphic mapping theory, non-smooth analysis, LMIs, free-weighting matrix and Lyapunov–krasovskii functional approach. Furthermore, the paper authored by R. Raja derived the stability analysis for a class of uncertain discrete-time stochastic BAM NNs with timevarying delays and impulses. Lyapunov–Krasovskii functional and stochastic analysis techniques were applied to obtain a set of sufficient conditions in term of LMI. Along this line, the non-stationary challenge in other class of NN can be tackled. The paper authored by Adel X.-Z. Wang A. B. Musa (&) Key Laboratory in Machine Learning and Computational Intelligence of Hebei Province, College of Mathematics and Computer Science, Hebei University, Baoding 071002, China e-mail: abdubashir20@yahoo.com

Exponential stability of impulsive discrete-time stochastic BAM neural networks with time-varying delay

In this paper, exponential stability of impulsive discrete-time stochastic bidirectional associative memory (BAM) neural networks with time-varying delay is investigated. Two sufficient conditions about exponential stability of this class of BAM neural networks are given by using difference inequalities and Lyapunov function together with Razumikhin technique. Some examples are also presented to illustrate the effectiveness and the advantage of the obtained results.

Exponential stability of stochastic higher-order BAM neural networks with reaction–diffusion terms and mixed time-varying delays

In this paper, we investigate the exponential stability of stochastic reaction–diffusion Bi-directional Associative Memory (BAM) neural networks. By constructing a novel Lyapunov–Krasovskii function, and applying inequality analysis technique as well as M-matrix theory, we first give some sufficient exponential stability criteria in terms of p-norm for a class of high-order stochastic reaction–diffusion BAM neural networks with discrete and distributed delays. The model we formulated is new and more general than the BAM neural networks investigated in previous publications. Moreover, the obtained results are easy to check and improve some existing stability results. An example is presented to show the application of the criteria obtained in this paper.

State estimation for switched discrete-time stochastic BAM neural networks with time varying delay

This paper focuses the issue of state estimation for a class of switched discrete-time stochastic bidirectional associative memory (BAM) neural networks with time varying delay. The main purpose of this paper is to estimate the neuron states through available output measurements such that the dynamics of the error state system to be robustly exponentially stable. By employing average dwell time approach together with piecewise Lyapunov functional technique, a set of sufficient conditions is derived with respect to all admissible uncertainties, to guarantee the existence of the desired state estimator for the uncertain switched discrete-time BAM delayed neural networks. Specifically, we derive sufficient conditions to achieve robust state estimation with the characterization of complex effects of time delays, parameter uncertainties, and stochastic perturbations. In particular, the parameter uncertainties are assumed to be time varying and unknown, but norm bounded. It should be mentioned that our estimation results are delay dependent, which depend on not only the upper bounds of time delay, but also their lower bounds. More precisely, the desired estimator matrix gain is obtained in terms of the solution of the derived LMIs. Finally, numerical examples with a simulation result are given to illustrate the effectiveness and applicability of the obtained results.

Stability analysis of Markovian jump stochastic BAM neural networks with impulse control and mixed time delays.

This paper discusses the issue of stability analysis for a class of impulsive stochastic bidirectional associative memory neural networks with both Markovian jump parameters and mixed time delays. The jumping parameters are modeled as a continuous-time discrete-state Markov chain. Based on a novel Lyapunov-Krasovskii functional, the generalized Itô's formula, mathematical induction, and stochastic analysis theory, a linear matrix inequality approach is developed to derive some novel sufficient conditions that guarantee the exponential stability in the mean square of the equilibrium point. At the same time, we also investigate the robustly exponential stability in the mean square of the corresponding system with unknown parameters. It should be mentioned that our stability results are delay-dependent, which depend on not only the upper bounds of time delays but also their lower bounds. Moreover, the derivatives of time delays are not necessarily zero or smaller than one since several free matrices are introduced in our results. Consequently, the results obtained in this paper are not only less conservative but also generalize and improve many earlier results. Finally, two numerical examples and their simulations are provided to show the effectiveness of the theoretical results.

Robust state estimation for uncertain stochastic bidirectional associative memory networks with time-varying delays

In this paper, we investigate the problem of robust state estimation for uncertain stochastic bidirectional associative memory (BAM) networks with time-varying delays. BAM networks are quite general and include parameter uncertainties, time-varying delays and stochastic disturbances. The activation functions are allowed to satisfy sector-like nonlinearities. The main purpose of investigating this problem is to design a linear estimator to approximate the state of the networks through available measurement outputs. By using the Lyapunov functional method and some stochastic analysis techniques, sufficient conditions are established in terms of linear matrix inequalities (LMIs) which can be checked easily by the Matlab toolbox. It is also shown that the designed state estimator can guarantee the estimation error dynamics to be globally robustly asymptotically stable in the mean square. Two illustrated examples are given to demonstrate the feasibility of the proposed estimation schemes.