Fuzzy Cohen-Grossberg Neural Networks Research Articles

Hyperbolic function-based fixed/preassigned-time stability of nonlinear systems and synchronization of delayed fuzzy Cohen–Grossberg neural networks

In this article, the fixed-time (FIT) and preassigned-time (PRT) stability of nonlinear models and the FIT/PRT synchronization of discontinuous delayed fuzzy Cohen–Grossberg neural networks (DFCGNNs) are explored, respectively. Firstly, by means of hyperbolic-cosine function and Gudermannian function, a novel FIT stability theorem is established by utilizing Lyapunov method. Then, based on the developed stability theorem, several new discontinuous control schemes with hyperbolic-cosine function are developed to discuss the FIT synchronization of DFCGNNs. Furthermore, the PRT synchronization is also explored by slightly modifying FIT control schemes, where the synchronization time is predetermined. Eventually, two numerical examples are provided to validate the theoretical research.

Fixed-Time Stabilization of Delayed Discontinuous Fuzzy Neural Networks via Delayed Stability Conditions of Filippov Systems

This article aims to propose time-delayed and simplified inequality conditions and establish more novel fixed-time (FXT) stability principles of delayed Filippov systems. First, the sign function is used to unify the orders of the Lyapunov–Krasovskii functional, and the time-delayed term is introduced in the inequality conditions, then some new FXT stability theorems are established and new estimations of the settling time involving delayed parameter are given that are absolutely different from the previous ones. The traditional inequality conditions <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\dot{V}(z)\leq -aV^\alpha (z)-bV^\beta (z)$</tex-math></inline-formula> is optimized and improved. For the purpose of illustrating the applicability, a class of delayed discontinuous fuzzy Cohen–Grossberg neural networks (DDFCGNNs) is studied. Some new criteria are derived, and the FXT stabilization of the addressed DDFCGNNs is achieved. Finally, a representative example and simulations are provided to examine the correctness.

Exponential stability and synchronisation of fuzzy Mittag–Leffler discrete-time Cohen–Grossberg neural networks with time delays

Exponential Euler differences for semi-linear differential equations of first order have got rapid development in the past few years and a variety of exponential Euler difference methods have become very significant researching topics. Therefore, exponential Euler differences for fractional-order differential models are novel and significant. In allusion to fuzzy Cohen–Grossberg neural networks of fractional order, this paper establishes a Mittag–Leffler Euler difference model on the basis of the constant variation formula in fractional calculus. In the second place, the existence of a unique global bounded solution and equilibrium point is studied by using the contractive mapping principle. Thirdly, global exponential stability and synchronisation of the derived difference models are investigated by employing some inequality techniques and reductio. At last, some illustrative examples and numerical simulations are employed to demonstrate the main results of this paper.

The synchronization and stability analysis of delayed fuzzy Cohen-Grossberg neural networks via nonlinear measure method

ABSTRACT This paper examines the problem of master-slave synchronization for a class of fuzzy Cohen-Grossberg neural networks (FCGNNs) subject to fuzzy effects and time-delays (time-varying and distributed). Some sufficient and new conditions are given in order to establish the exponential lag synchronization for the considered model. Also, the existence, the uniqueness, and exponential stability of the equilibrium point are investigated, based on the nonlinear measure method and Halanay inequality. Finally, two examples with numerical simulations are given to show the effectiveness of the derived results.

Finite-time and fixed-time synchronization control of discontinuous fuzzy Cohen-Grossberg neural networks with uncertain external perturbations and mixed time delays

This paper aims to investigate the synchronization control of a class of discontinuous fuzzy Cohen-Grossberg neural networks (DFCGNNs) with uncertain external perturbations and mixed time delays (discrete and distributed time-delays). By using functional differential inclusions theory, inequality technique and the non-smooth analysis of Lyapunov-Krasovskii functional, a simple switching adaptive control is designed and some new criteria are obtained to achieve the finite-time synchronization of the proposed drive-response systems. Besides, the upper bound of the settling time is estimated. Based on the finite-time synchronization, we further present a novel discontinuous state-feedback controller to the response neural system in order to derive the fixed-time synchronization criteria and estimate the settling time. Compared with the previous results which can only fixed-timely synchronize or finite-timely synchronize some simple delayed fuzzy neural network systems with continuous activation functions and without uncertain external perturbations, the DFCGNNs with uncertain external perturbations and mixed time delays addressed and the theoretical results of this paper are more generalized and inclusive. Finally, several simulation examples and remarks are provided to verify the correctness and advantages of the main results.

Stability analysis of delayed fuzzy Cohen‐Grossberg neural networks with discontinuous activations

SummaryIn this article, we investigate the dynamical behavior of a class of delayed fuzzy Cohen‐Grossberg neural networks (FCGNNs) with discontinuous activation functions subject to time delays and fuzzy terms. By using the inequality analysis technique and the M‐matrix theory, sufficient and proper conditions are given in order to establish the existence, convergence, and global exponential stability of equilibrium point of the system. In particular, we discuss the impact of discontinuous neuron activations on the existence and exponential stability of equilibrium point for FCGNNs. Two numerical examples are provided to substantiate the theoretical results.

Graph-Theoretic Approach to Finite-Time Synchronization for Fuzzy Cohen–Grossberg Neural Networks with Mixed Delays and Discontinuous Activations

This paper investigates finite-time synchronization for fuzzy Cohen–Grossberg neural networks (FCGNNs) with mixed delays and discontinuous activations via state-feedback control. The features of FCGNNs, discrete time delays, distributed delays and discontinuous activations are taken into account which makes our networks more general and practical in comparison with the most existing Cohen–Grossberg neural networks. Two switching state-feedback controllers designed for the implement of finite-time synchronization can be used to effectively overcome the limitations of the traditional continuous linear feedback controllers. Different from previous work, graph theory and Lyapunov method are used to study finite-time synchronization of FCGNNs for the first time in this paper, then some sufficient criteria are obtained to guarantee the finite-time synchronization of FCGNNs. In particular, it is worth noting that the settling time for finite-time synchronization is closely related to the topological structure of FCNNs. Finally, two numerical examples are given to verify the feasibility and effectiveness of the theoretical results.

Finite-time and fixed-time synchronization analysis of fuzzy Cohen–Grossberg neural networks with discontinuous activations and parameter uncertainties

This paper mainly investigates the finite-time and fixed-time synchronization for a class of delayed fuzzy Cohen–Grossberg neural networks with discontinuous activations and parameter uncertainties. First of all, the equivalent transformation is made for the proposed neural network system in order to deal with the amplification functions. By using the Filippov discontinuity theories and non-smooth Lyapunov–Krasovskii functional, some sufficient algebraic criteria are given for the selection of the designed switching adaptive control parameters to accomplish the finite-time synchronization, and the upper bound of the settling time can be estimated. After that, based on the inequality technique and by designing a discontinuous state-feedback control law, some sufficient conditions are derived to achieve synchronization within a fixed time, and the settling time is given, which is independent on initial values. The Cohen–Grossberg neural networks combining fuzzy model with discontinuous activations and parameter uncertainties are considered for the first time in the literature. Finally, a numerical example is presented to illustrate the effectiveness of the proposed synchronization strategies.

Piecewise asymptotic almost periodic solutions for impulsive fuzzy Cohen–Grossberg neural networks

Abstract In this paper, we propose a new class of impulsive fuzzy Cohen–Grossberg neural networks (FCGNNs) with delays. It is well known that time delays and external impulsive can derail the stability of a given dynamical system and a fortiori in neural networks. Hence, in this paper, by designing a novel and adequate Lyapunov functional and using an appropriate fixed point theorem we derive several new sufficient conditions for the existence, uniqueness and global exponential stability of the considered model. Moreover, two numerical examples are given in order to illustrate the effectiveness of our theoretical results.

Exponential Lag Synchronization and Global Dissipativity for Delayed Fuzzy Cohen–Grossberg Neural Networks with Discontinuous Activations

This paper investigates the qualitative behavior of a new class of fuzzy Cohen–Grossberg neural networks with discontinuous neuron activations and mixed delays. Roughly speaking, some novel sufficient conditions are established in order to demonstrate the global dissipativity and the exponential lag synchronization of the considered model by using the theory of Filippov systems and Lyapunov method. Finally, two examples are presented to show the effectiveness of the obtained results.

Finite-time and fixed-time synchronization control of fuzzy Cohen-Grossberg neural networks

This paper aims to investigate the finite-time and fixed-time robust synchronization of fuzzy Cohen-Grossberg neural networks with discontinuous activations. To deal with the discontinuous property, the framework of Filippov solution is invoked to solve the inexistence of the classical solutions. For the purpose of achieving fixed-time synchronization, we turn to investigating the fixed-time stability problem of the error system between the drive-response systems. By the functional differential inclusions theory, inequality technique and the non-smooth Lyapunov-Krasovskii functional and designing a simple discontinuous state-feedback control law for the response neural system, some sufficient algebraic criteria are derived to achieve synchronization within a fixed time, and the settling time is given. Moreover, based on the fixed-time robust synchronization and under the same basic assumptions, we further complete the finite-time synchronization of the addressed drive-response systems by designing a simple switching adaptive controller, and the upper bound of the settling time is also estimated. It should be regarded as the first time to study the finite-time synchronization of fuzzy Cohen-Grossberg neural networks with discontinuous activations based on the adaptive control. Finally, some numerical examples are presented to illustrate the effectiveness of the proposed synchronization strategies.

New stability results for Takagi–Sugeno fuzzy Cohen–Grossberg neural networks with multiple delays

This work focuses on global asymptotic stability of Takagi–Sugeno fuzzy Cohen–Grossberg neural networks with multiple time delays. By using the standard Lyapunov stability techniques and nonsingular M-matrix condition of matrices together with employing the nonlinear Lipschitz activation functions, a new easily verifiable sufficient criterion is obtained to guarantee global asymptotic stability of the Cohen–Grossberg neural network model which is represented by a Takagi–Sugeno fuzzy model. A constructive numerical example is studied to demonstrate the effectiveness of the proposed theoretical results. This numerical example is also used to make a comparison between the global stability condition obtained in this study and some of previously published global stability results. This comparison reveals that the condition we propose establishes a novel and alternative stability result for Takagi–Sugeno fuzzy Cohen–Grossberg neural networks of this class.

Input-to-state stability of stochastic nonlinear fuzzy Cohen–Grossberg neural networks with the event-triggered control

ABSTRACT In this paper, we investigate a class of stochastic nonlinear fuzzy Cohen–Grossberg neural networks with feedback control and an unknown exogenous disturbance. By using the Lyapunov function, Itô's formula, Dynkin's formula, Comparison principle and stochastic analysis theory, we show that the considered system is input-to-state stable with the help of the designed event-triggered mechanism. Moreover, we also guarantee that the internal execution time intervals of control task will not be arbitrarily small. Finally, some remarks and discussions have been provided to show that our results are meaningful.

An improved stability result for delayed Takagi–Sugeno fuzzy Cohen–Grossberg neural networks

This work proposes a novel and improved delay independent global asymptotic stability criterion for delayed Takagi–Sugeno (T–S) fuzzy Cohen–Grossberg neural networks exploiting a suitable fuzzy-type Lyapunov functional in the presence of the nondecreasing activation functions having bounded slopes. The proposed stability criterion can be easily validated as it is completely expressed in terms of the system matrices of the fuzzy neural network model considered. It will be shown that the stability criterion obtained in this work for this type of fuzzy neural networks improves and generalizes some of the previously published stability results. A constructive numerical example is also given to support the proposed theoretical results.

TAKAGİ-SUGENO BULANIK COHEN-GROSSBERG TİPİ ZAMAN GECİKMELİ YAPAY SİNİR AĞLARINDA KARARLILIK ANALİZİ

This paper deals with the problem of the global asymptotic stability of the class of Takagi-Sugeno Fuzzy Cohen-Grossberg neural networks with multiple time delays. By constructing a suitable fuzzy Lyapunov functional, we present a new delay-independent sufficient condition for the global asymptotic stability of the equilibrium point for delayed Takagi-Sugeno Fuzzy Cohen-Grossberg neural networks with respect to the Lipschitz activation functions. The obtained condition simply relies on the network parameters of the neural system. Therefore, the equilibrium and stability properties of the neural network model considered in this paper can be easily verified by exploiting some basic properties of some certain classes of matrices.

An Analysis of Global Stability of Takagi–Sugeno Fuzzy Cohen–Grossberg Neural Networks with Time Delays

This paper deals with the problem of the global asymptotic stability of Takagi–Sugeno (T–S) fuzzy Cohen–Grossberg neural networks with multiple time delays. By using Lyapunov method and some basic properties of matrices, and employing the nondecreasing and slope-bounded activation functions, an easily verifiable sufficient criterion is derived to establish the asymptotic stability of a general class of (T–S) fuzzy Cohen–Grossberg neural networks with multiple time delays. The obtained stability condition establishes some relationships between the network parameters of the neural network model independently of the delay parameters. A numerical example is also given to illustrate the effectiveness of the theoretical results.

Mittag-Leffler stability analysis of fractional-order fuzzy Cohen-Grossberg neural networks with deviating argument

This paper is concerned with the Mittag-Leffler stability of fractional-order fuzzy Cohen-Grossberg neural networks with deviating argument. Applying the Lyapunov method, the generalized Gronwall-Bellman inequality, and the theory of fractional-order differential equations, sufficient conditions are presented to guarantee the existence and uniqueness of solution. Besides, the global Mittag-Leffler stability is investigated. The obtained criteria are useful in the analysis and design of fractional-order fuzzy Cohen-Grossberg neural networks with deviating argument. A numerical example is given to substantiate the validity of the theoretical results.

Pth moment exponential stability of stochastic fuzzy Cohen–Grossberg neural networks with discrete and distributed delays

In this paper, stochastic fuzzy Cohen–Grossberg neural networks with discrete and distributed delays are investigated. By using Lyapunov function and the Ito differential formula, some sufficient conditions for the pth moment exponential stability of such stochastic fuzzy Cohen–Grossberg neural networks with discrete and distributed delays are established. An example is given to illustrate the feasibility of our main theoretical findings. Finally, the paper ends with a brief conclusion. Methodology and achieved results is to be presented.

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.

New Stability Criterion for Takagi-Sugeno Fuzzy Cohen-Grossberg Neural Networks with Probabilistic Time-Varying Delays

A new global asymptotic stability criterion of Takagi-Sugeno fuzzy Cohen-Grossberg neural networks with probabilistic time-varying delays was derived, in which the diffusion item can play its role. Owing to deleting the boundedness conditions on amplification functions, the main result is a novelty to some extent. Besides, there is another novelty in methods, for Lyapunov-Krasovskii functional is the positive definite form of p powers, which is different from those of existing literature. Moreover, a numerical example illustrates the effectiveness of the proposed methods.