Fuzzy Bidirectional Associative Memory Research Articles

Global Asymptotic Stability and Synchronization of Fractional-Order Reaction–Diffusion Fuzzy BAM Neural Networks with Distributed Delays via Hybrid Feedback Controllers

In this paper, the global asymptotic stability and global Mittag–Leffler stability of a class of fractional-order fuzzy bidirectional associative memory (BAM) neural networks with distributed delays is investigated. Necessary conditions are obtained by means of the Lyapunov functional method and inequality techniques. The hybrid feedback controllers are then developed to ensure the global asymptotic synchronization of these neural networks, resulting in two additional synchronization criteria. The derived conditions are applied to check the fractional-order fuzzy BAM neural network’s Mittag–Leffler stability and synchronization. Three examples are given to demonstrate the effectiveness of the achieved results.

Global Exponential Stability and Synchronization of Discrete-Time Fuzzy Bidirectional Associative Memory Neural Networks via Mittag-Leffler Difference Approach

Global Exponential Stability and Synchronization of Discrete-Time Fuzzy Bidirectional Associative Memory Neural Networks via Mittag-Leffler Difference Approach

Predefined-Time (PDT) Synchronization of Impulsive Fuzzy BAM Neural Networks with Stochastic Perturbations

This paper focuses on the predefined-time (PDT) synchronization issue of impulsive fuzzy bidirectional associative memory neural networks with stochastic perturbations. Firstly, useful definitions and lemmas are introduced to define the PDT synchronization of the considered system. Next, a novel controller with a discontinuous sign function is designed to ensure the synchronization error converges to zero in the preassigned time. However, the sign function may cause the chattering effect, leading to undesirable results such as the performance degradation of synchronization. Hence, we designed a second novel controller to eliminate this chattering effect. After that, we obtained some sufficient conditions to guarantee the PDT synchronization of the drive–response systems by using the Lyapunov function method. Finally, three numerical simulations are provided to evaluate the validity of the theoretical results.

PERIODIC DYNAMICS AND MEAN-SQUARE EXPONENTIAL CONVERGENCE OF NONLOCAL STOCHASTIC FUZZY BIDIRECTIONAL ASSOCIATIVE MEMORY LATTICE NEURAL NETWORKS

This paper firstly establishes the lattice model for nonlocal stochastic fuzzy bidirectional associative memory neural networks with reaction diffusions by employing a mix of the finite difference and Mittag-Leffler time Euler difference techniques. Secondly, the existence of a unique bounded periodic sequence solution in distribution and global mean-square exponential convergence to the achieved difference model are investigated. Some illustrative example is used to show the feasible of the works of the current paper.

Robustness analysis of fuzzy BAM cellular neural network with time-varying delays and stochastic disturbances

<abstract><p>Robustness analysis for the global exponential stability of fuzzy bidirectional associative memory cellular neural network (FBAMCNN) is explored in this paper. By applying Gronwall-Bellman lemma and other inequality techniques, the range limits of both time-varying delays and the intensity of noise that FBAMCNN can withstand to maintain globally exponentially stable is estimated. It means that if the intensities of interference are larger than the bounds we derived, then the perturbed system may lose global exponential stability. Several instances are given to support our main results.</p></abstract>

Finite-time stochastic synchronization of fuzzy bi-directional associative memory neural networks with Markovian switching and mixed time delays via intermittent quantized control

<abstract><p>We are concerned in this paper with the finite-time synchronization problem for fuzzy bi-directional associative memory neural networks with Markovian switching, discrete-time delay in leakage terms, continuous-time and infinitely distributed delays in transmission terms. After detailed analysis, we come up with an intermittent quantized control for the concerned bi-directional associative memory neural network. By designing an elaborate Lyapunov-Krasovskii functional, we prove under certain additional conditions that the controlled network is stochastically synchronizable in finite time: The $ 1 $st moment of every trajectory of the error network system associated to the concerned controlled network tends to zero as time approaches a finite instant (the settling time) which is given explicitly, and remains to be zero constantly thereupon. In the meantime, we present a numerical example to illustrate that the synchronization control designed in this paper is indeed effective. Since the concerned fuzzy network includes Markovian jumping and several types of delays simultaneously, and it can be synchronized in finite time by our suggested control, as well as the suggested intermittent control is quantized which could reduce significantly the control cost, the theoretical results in this paper are rich in mathematical implication and have wide potential applicability in the real world.</p></abstract>

Global dissipativity of fuzzy bidirectional associative memory neural networks with proportional delays

This article aimed to investigate the problem of global dissipativity of Fuzzy Bidirectional Associative Memory Neural Networks (FBAMNNs- for short) with proportional delays. Via Lyapunov Functionals (LFs- for short) and Linear Matrix Inequality (LMI- for short) approach, we obtained new sufficient conditions to guarantee the global dissipativity and global exponential dissipativity of the proposed model. In addition, two different types of activation functions are considered, including general bounded and Lipschitz-type activation functions. Moreover, the globally attractive and globally exponentially attractive sets are presented. Lastly, two numerical examples are given to illustrate the effectiveness of the developed results.

Designing Intelligent MIMO Nonlinear Controller Based on Fuzzy Cognitive Map Method for Energy Reduction of the Buildings

Designing a suitable controller for air-conditioning systems to reduce energy consumption and simultaneously meet the requirements of the system is very challenging. Important factors such as stability and performance of the designed controllers should be investigated to ensure the effectiveness of these controllers. In this article, the stability and performance of the fuzzy cognitive map (FCM) controller are investigated. The FCM method is used to control the direct expansion air conditioning system (DX A/C). The FCM controller has the ability to do online learning, and can achieve fast convergence thanks to its simple mathematical computation. The stability analysis of the controller was conducted using both fuzzy bidirectional associative memories (FBAMs) and the Lyapunov function. The performances of the controller were tested based on its ability for reference tracking and disturbance rejection. On the basis of the stability analysis using FBAMS and Lyapunov functions, the system is globally stable. The controller is able to track the set point faithfully, maintaining the temperature and humidity at the desired value. In order to simulate the disturbances, heat and moisture load changed to measure the ability of the controller to reject the disturbance. The results showed that the proposed controller can track the set point and has a good ability for disturbance rejection, making it an effective controller to be employed in the DX A/C system and suitable for a nonlinear robust control system.

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.

Fixed-Time Synchronization of Memristive Fuzzy BAM Cellular Neural Networks With Time-Varying Delays Based on Feedback Controllers

This paper mainly investigates the fixed-time synchronization problem of memristive fuzzy bidirectional associative memory (BAM) cellular neural networks (MFBAMCNNs) with time-varying delays. MFBAMCNNs are formulated by virtue of differential inclusion and set-valued map theories. By utilizing the definition of fixed-time synchronization and some inequality techniques, some novel criteria for easy verification are derived to ensure the fixed-time synchronization of the drive-response MFBAMCNNs based on the Lyapunov stability theory and nonlinear feedback controllers. The results of the main theorem can be easily extended to the fuzzy BAM cellular neural networks without memristor and the memristive BAM cellular neural networks without fuzzy logic. In addition, the settling time of fixed-time synchronization, which does not depend on the initial values, can be simply calculated. At last, two numerical examples are presented to verify the effectiveness of main results.

Exponential stability criteria for fuzzy bidirectional associative memory Cohen-Grossberg neural networks with mixed delays and impulses

This paper is concerned with fuzzy bidirectional associative memory (BAM) Cohen-Grossberg neural networks with mixed delays and impulses. By constructing an appropriate Lyapunov function and a new differential inequality, we obtain some sufficient conditions which ensure the existence and global exponential stability of a periodic solution of the model. The results in this paper extend and complement the previous publications. An example is given to illustrate the effectiveness of our obtained results.

Synchronization of fuzzy bidirectional associative memory neural networks with various time delays

The problem of synchronization for fuzzy bidirectional associative memory (BAM) neural networks (NNs) with various time delays is formulated and investigated. The various delays consist of discrete delays, unbounded distributed delays and constant delay in the leakage term (i.e. ‘leakage delay’) are considered. Then, some sufficient conditions are presented to guarantee the global asymptotic stability of the error dynamical system by using Lyapunov–Krasovskii functional and linear matrix inequality (LMI) method. As a result, we achieved synchronization of master-slave (drive-response) fuzzy BAM NNs systems. Even, if there is no leakage delay, the obtained results are less restrictive to some known sufficient conditions. Moreover, the proposed results do not require the boundedness, differentiability and monotonicity of the activation functions, which can also be easily checked via the LMI solver in robust control toolbox in Matlab. Furthermore, using a parameter-dependent Lyapunov function approach the synchronization problem for polytopic uncertain fuzzy BAM NNs with various time delays is considered. The parameter uncertainties under consideration are assumed to belong to a fixed convex polytope. Finally, two numerical examples and simulations are given to illustrate the effectiveness of the derived theoretical 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 state estimation for uncertain fuzzy bidirectional associative memory networks with time-varying delays

This paper addresses the issue of robust state estimation for a class of fuzzy bidirectional associative memory (BAM) neural networks with time-varying delays and parameter uncertainties. By constructing the Lyapunov–Krasovskii functional, which contains the triple-integral term and using the free-weighting matrix technique, a set of sufficient conditions are derived in terms of linear matrix inequalities (LMIs) to estimate the neuron states through available output measurements such that the dynamics of the estimation error system is robustly asymptotically stable. In particular, we consider a generalized activation function in which the traditional assumptions on the boundedness, monotony and differentiability of the activation functions are removed. More precisely, the design of the state estimator for such BAM neural networks can be obtained by solving some LMIs, which are dependent on the size of the time derivative of the time-varying delays. Finally, a numerical example with simulation result is given to illustrate the obtained theoretical results.

Existence and exponential stability of an equilibrium point for fuzzy BAM neural networks with time-varying delays in leakage terms on time scales

In this paper, by using a fixed point theorem and differential inequality techniques, we consider the existence and global exponential stability of an equilibrium point for a class of fuzzy bidirectional associative memory neural networks with time-varying delays in leakage terms on time scales. We also present a numerical example to show the feasibility of obtained results. The results of this paper are completely new and complementary to the previously known results.MSC:34B37, 34N05.

New Passivity Criteria for Fuzzy Bam Neural Networks with Markovian Jumping Parameters and Time-Varying Delays

This paper addresses the problem of passivity analysis issue for a class of fuzzy bidirectional associative memory (BAM) neural networks with Markovian jumping parameters and time varying delays. A set of sufficient conditions for the passiveness of the considered fuzzy BAM neural network model is derived in terms of linear matrix inequalities by using the delay fractioning technique together with the Lyapunov function approach. In addition, the uncertainties are inevitable in neural networks because of the existence of modeling errors and external disturbance. Further, this result is extended to study the robust passivity criteria for uncertain fuzzy BAM neural networks with time varying delays and uncertainties. These criteria are expressed in the form of linear matrix inequalities (LMIs), which can be efficiently solved via standard numerical software. Two numerical examples are provided to demonstrate the effectiveness of the obtained results.

Global Exponential Stability of Fuzzy BAM Neural Networks with Distributed Delays

In this paper, by using the theory of topological degree, Lyapunov functional and analysis technique, the sufficient conditions which ensure the existence, uniqueness and global exponential stability of the equilibrium point for fuzzy bi-directional associative memory neural networks with distributed delays are obtained. The results remove the usual assumption that the activation functions are bounded. An example is given to illustrate the effectiveness and feasibility of results obtained.

Dynamics of fuzzy impulsive bidirectional associative memory neural networks with time-varying delays

Complex nonlinear systems can be represented to a set of linear sub-models by using fuzzy sets and fuzzy reasoning via ordinary Takagi-Sugeno (TS) fuzzy models. In this paper, the exponential stability of TS fuzzy bidirectional associative memory (BAM) neural networks with impulsive effect and time-varying delays is investigated. The model of fuzzy impulsive BAM neural networks with time-varying delays established as a modified TS fuzzy model is new in which the consequent parts are composed of a set of impulsive BAM neural networks with time-varying delays. Further the exponential stability for fuzzy impulsive BAM neural networks is presented by utilizing the Lyapunov-Krasovskii functional and the linear matrix inequality (LMI) technique without tuning any parameters. In addition, an example is provided to illustrate the applicability of the result using LMI control toolbox in MATLAB.

Stability results for Takagi–Sugeno fuzzy uncertain BAM neural networks with time delays in the leakage term

This paper deals with the delay-dependent asymptotic stability analysis problem for a class of fuzzy bidirectional associative memory (BAM) neural networks with time delays in the leakage term by Takagi–Sugeno (T–S) fuzzy model. The nonlinear delayed BAM neural networks are first established as a modified T–S fuzzy model in which the consequent parts are composed of a set of BAM neural networks with time-varying delays. The parameter uncertainties are assumed to be norm bounded. Some new delay-dependent stability conditions are derived in terms of linear matrix inequality by constructing a new Lyapunov–Krasovskii functional and introducing some free-weighting matrices. Even there is no leakage delay, the obtained results are also less restrictive than some recent works. It can be applied to BAM neural networks with activation functions without assuming their boundedness, monotonicity, or differentiability. Numerical examples are given to demonstrate the effectiveness of the proposed methods.

EXISTENCE AND GLOBALLY EXPONENTIAL STABILITY OF PERIODIC SOLUTION OF IMPULSIVE FUZZY BAM NEURAL NETWORKS WITH DISTRIBUTED DELAYS AND VARIABLE COEFFICIENTS

In this paper, a class of impulsive fuzzy bi-directional associative memory (BAM) neural networks with distributed delays and variable coefficients are considered. Using Lyapunov functional method and fixed point theorem, we derived some sufficient conditions for the existence and globally exponential stability of unique periodic solution of the networks. The results obtained are new and extend the previous known results. In addition, an example is given to show the effectiveness of our results obtained.