Fuzzy Cellular Neural Networks Research Articles

Exponential Quasi-Synchronization of Fractional-Order Fuzzy Cellular Neural Networks via Impulsive Control

This paper investigates the exponential quasi-synchronization of fractional-order fuzzy cellular neural networks with parameters mismatch via impulsive control. Firstly, under the framework of the generalized Caputo fractional-order derivative, a new fractional-order impulsive differential inequality is established. Secondly, based on this fractional-order impulsive differential inequality, a general criterion for the quasi-synchronization of fractional-order systems is obtained. Then, specific to the fractional-order fuzzy cellular neural network model in this paper, the criteria and error estimation of the exponential quasi-synchronization of fractional-order fuzzy cellular neural networks can be obtained. Finally, two numerical examples are given to illustrate the effectiveness of the obtained results.

Polynomial synchronization of quaternion-valued fuzzy cellular neural networks with proportional delays

Polynomial synchronization of quaternion-valued fuzzy cellular neural networks with proportional delays

Improved fixed-time stability analysis and applications to synchronization of discontinuous complex-valued fuzzy cellular neural networks

This article mainly centers on proposing new fixed-time (FXT) stability lemmas of discontinuous systems, in which novel optimization approaches are utilized and more relaxed conditions are required. The conventional discussions about Vt>1 and 0<Vt⩽1 are no longer required. For the purpose of verifying the new lemmas, complex-valued fuzzy cellular neural networks (CVFCNNs) with discontinuous activation functions are studied with a nontraditional non-separation method, which could reduce the conservatism of the obtained results greatly. Besides, FXT synchronization is discussed simultaneously. When contrasted with the results of other similar prominent pioneering works nowadays, the accuracy of settling times (STs) is quite enhanced. At last, numerical simulations are conducted to demonstrate the validity and superiority of our established theoretical results.

Quasi-projective Synchronization Control of Delayed Stochastic Quaternion-Valued Fuzzy Cellular Neural Networks with Mismatched Parameters

Quasi-projective Synchronization Control of Delayed Stochastic Quaternion-Valued Fuzzy Cellular Neural Networks with Mismatched Parameters

Practical finite-time synchronization of delayed fuzzy cellular neural networks with fractional-order

The practical finite-time (PFT) synchronization of fractional-order delayed fuzzy cellular neural networks (FODFCNNs) is presented in this article. Initially, a useful practical finite time (FT) stable lemma is developed, serving as an efficient instrument for the PFT synchronization of fractional-order systems. Subsequently, a new PFT synchronization criterion for FODFCNNs is derived using the designed controller and the aforementioned lemma. Simultaneously, the settling time for PFT synchronization is determined, relying on specific controller parameters and the initial conditions of the considered systems. Ultimately, the accuracy of the derived outcomes is confirmed through a numerical simulation.

Global robust stability of fuzzy cellular neural networks with parameter uncertainties

&lt;abstract&gt;&lt;p&gt;The global robust stability of uncertain delayed fuzzy cellular neural networks (UDFCNNs) was analyzed in this paper. The major results of this paper provided some new criteria for the existence and uniqueness of the equilibrium point of UDFCNN. Furthermore, suitable Lyapunov-Krasovskii functionals was designed for obtaining the adequate conditions for the global asymptotic robust stability and global exponential robust stability of UDFCNN. Finally, several numerical examples was provided to verify the validity of the results.&lt;/p&gt;&lt;/abstract&gt;

Novel fixed-time synchronization results of fractional-order fuzzy cellular neural networks with delays and interactions

&lt;abstract&gt;&lt;p&gt;This research investigated the fixed-time (FXT) synchronization of fractional-order fuzzy cellular neural networks (FCNNs) with delays and interactions based on an enhanced FXT stability theorem. By conceiving proper Lyapunov functions and applying inequality techniques, several sufficient conditions were obtained to vouch for the fixed-time synchronization (FXTS) of the discussed systems through two categories of control schemes. Moreover, in terms of another FXT stability theorem, different upper-bounding estimating formulas for settling time (ST) were given, and the distinctions between them were pointed out. Two examples were delivered at length to demonstrate the conclusions.&lt;/p&gt;&lt;/abstract&gt;

Finite-Time Synchronization of Fractional-Order Delayed Fuzzy Cellular Neural Networks With Parameter Uncertainties

The finite-time synchronization (FTS) is studied for a class of fractional-order delayed fuzzy cellular neural networks (FODFCNNs) with parameter uncertainties. A linear fractional-order finite time inequality (FOFTI) <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${}^{c}_{t_{0}}D^{p}_{t} V(t)\le -a V(t)-b$</tex-math></inline-formula> is extended to the nonlinear case <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${}^{c}_{t_{0}}D^{p}_{t} V(t)\le -a V^{-\eta }(t)-b$</tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\eta \ge 1$</tex-math></inline-formula> , which plays a vital role in the FTS of fractional-order systems. However, for the case of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$0&lt; \eta &lt; 1$</tex-math></inline-formula> , a theoretical cornerstone justifying its use is still missing. To fill this research gap, on the basis of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$C_{p}$</tex-math></inline-formula> inequality and the rule for fractional-order derivative of composite function, a nonlinear FOFTI <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${}^{c}_{t_{0}}D^{p}_{t} V(t)\le -a V^{-\eta }(t)-b$</tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$0&lt; \eta &lt; 1$</tex-math></inline-formula> is developed. Furthermore, a nonlinear FOFTI <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${}^{c}_{t_{0}}D^{p}_{t} V(t)\le -bV^{-\xi }(t)-a V^{-\eta }(t)$</tex-math></inline-formula> is also established. These two novel inequalities provide the new tools for the research on the finite time stability and synchronization of fractional-order systems and can greatly extend the pioneer ones. Next, on the basis of these novel inequalities, the feedback controller is designed and two novel FTS criteria of FODFCNNs with parameter uncertainties are obtained. Finally, two examples are presented to verify the effectiveness of the derived results.

Besicovitch-like almost periodic solutions of Clifford-valued fuzzy cellular neural networks with time-varying delays

In this paper, we are concerned with a class of Clifford-valued fuzzy cellular neural networks with time-varying delays. Based on the Banach fixed point theorem and inequality technique, we obtain the existence and uniqueness of Besicovitch-like almost periodic solutions and global exponential stability of the fuzzy cellular neural network under consideration. Finally, we give a numerical example to illustrate the effectiveness of our results. Even when the systems we consider degenerate to quaternion-valued, complex-valued and real-valued ones, our results in this paper are completely new.

Adaptive finite-time synchronization of fractional-order delayed fuzzy cellular neural networks

The adaptive finite-time synchronization problems are investigated for a class of fractional-order delayed fuzzy cellular neural networks (FODFCNNs). First, with the aid of the properties of the Mittag-Leffler function and the Laplace transform with the parameter, some novel fractional-order differential inequalities are established to provide new perspective to explore finite-time synchronization of fractional-order systems. Second, based on these inequalities and the designed adaptive controller, some novel sufficient conditions are given to guarantee the adaptive finite-time synchronization of FODFCNNs. Finally, the effectiveness of the results is demonstrated by a numerical example.

Robustness Analysis of Fuzzy Cellular Neural Network With Deviating Argument and Stochastic Disturbances

Robustness analysis of fuzzy cellular neural networks with deviating arguments and stochastic disturbances is the main topic of discussion in this paper. The issue at hand is what the upper bounds of the disturbances and deviating intervals for the fuzzy cellular neural network can withstand before losing its stability. We solve these problems by using Gronwall-Bellman lemma and some inequality techniques. The theoretical results point that for an exponentially stable fuzzy cellular neural network, the perturbed fuzzy cellular neural network still keep its globally exponential stability if the upper bound of the length of deviating intervals or the intensity of stochastic disturbances is less than the upper bound derived in this paper. A number of numerical cases are offered to support the availability of conjectural values.

Cryptanalysis of various images based on neural networks with leakage and time varying delays

Abstract The main objective of this paper is to provide an efficient image encryption for each and every single person in order to secure their own records while saving them in social networks. We have formulated the delayed fuzzy cellular neural networks (FCNNs) with suitable keys that are the values of the parameters of FCNNs and obtain the irregular dynamical signal (solution) which encrypts the images. We have utilized entirely 42 parameters as a key sensitivity in the order of 10−15 among them three elements of initial condition parameters are sensitive to the order of 10−14. Lastly, comparison results are provided with the existing literature. The measurements show that the proposed algorithm is a novel overall solution for image encryption.

Anti-periodic solutions of Clifford-valued fuzzy cellular neural networks with delays

Anti-periodic solutions of Clifford-valued fuzzy cellular neural networks with delays

An improved criterion on finite-time stability for fractional-order fuzzy cellular neural networks involving leakage and discrete delays

This paper concentrates on the finite-time stability (FTS) for fractional-order fuzzy cellular neural networks involving leakage and discrete delays. We propose a method to develop a new FTS criterion which is a supplement to the research on stability for fractional-order systems. The proof mainly depends on a new Henry–Gronwall integral inequality (HGII) with two discrete delays. This inequality generalizes some known ones which have played a significant role in the analysis on fractional-order systems. Finally, we demonstrate the correctness and advantages of the obtained criterion by supplying some examples.

Exponential Synchronization of Inertial Complex-Valued Fuzzy Cellular Neural Networks with Time-Varying Delays via Periodically Intermittent Control

This paper mainly studies the exponential synchronization issue for the inertial complex-valued fuzzy cellular neural networks (ICVFCNNs) with time-varying delays via periodically intermittent control. To achieve exponential synchronization, we use a non-reduced order and non-separation approach, which is a supplement and innovation to the previous method. Based on directly constructing Lyapunov functional and a novel periodically intermittent control scheme, sufficient conditions for achieving the exponential synchronization of the ICVFCNNs are established. Finally, an example is given to illustrate the validity of the obtained results.

Synchronization in Finite Time of Fuzzy Neural Networks with Hybrid Delays and Uncertain Nonlinear Perturbations

This paper deals with the finite-time synchronization problem of a class of fuzzy neural networks with hybrid delays and uncertain nonlinear perturbations. By applying the famous finite-time stability theory, combining differential inequality techniques, and the analysis approach, several new algebraic sufficient criteria are obtained to realize finite-time synchronization between the drive system and the response system by designing a state feedback controller and an adaptive controller. Taking discrete delays, distributed delays, and uncertain nonlinear perturbations into account in fuzzy cellular neural networks makes the neural system more general than most existing cellular neural networks. Two different novel types of controllers designed to achieve finite-time synchronization can not only effectively overcome the influence of time delays and perturbations but also change their form according to the change of system state or perturbation to achieve a better control effect. Meanwhile, some algebraic sufficient criteria obtained in this paper can be proved by the parameters of the system itself, and the complex calculation of matrix inequality is avoided. Finally, the validity of our proposed results is confirmed by several examples and simulations. Furthermore, a secure communication problem is presented to further illustrate the fact of the obtained results.

Preassigned-Time Synchronization of Delayed Fuzzy Cellular Neural Networks with Discontinuous Activations

Preassigned-Time Synchronization of Delayed Fuzzy Cellular Neural Networks with Discontinuous Activations

Global quasi-synchronisation of fuzzy cellular neural networks with time varying delay and interaction terms

In this article, the global quasi-synchronisation of fuzzy cellular neural networks (FCNNs) in the presence of interaction terms and time-varying delay has been studied. The quasi-synchronisation criteria of FCNNs have been found with the help of p-norm and inequalities defined in Lemmas 2.1 and 2.2. Under the Lyapunov stability theory, the quasi-synchronisation of fuzzy-based CNNs with time-varying delay and interaction terms is attained using state-feedback controllers. A significant result for the two nonidentical FCNNs with time varying delay and interaction terms is provided. The error bounds of the global quasi-synchronisation have also been estimated. It is also seen that the global quasi-synchronisation of FCNNs is quite new. Two numerical simulation results are given to exhibit the viability and unwavering quality of the obtained results under several conditions.

Global asymptotic stability of delayed fractional-order complex-valued fuzzy cellular neural networks with impulsive disturbances

Global asymptotic stability of delayed fractional-order complex-valued fuzzy cellular neural networks with impulsive disturbances

Passivity Analysis of Fractional-Order Neutral-Type Fuzzy Cellular BAM Neural Networks with Time-Varying Delays

In this paper, passivity analysis of fractional-order neutral-type fuzzy cellular bidirectional associative memory (BAM) neural networks with time-varying delays is investigated. Based on the Lyapunov–Krasovskii functional, delay-dependent sufficient conditions for solvability of the passive problem are obtained in terms of linear matrix inequalities (LMIs), which can be easily checked by using the MATLAB LMI toolbox. Finally, numerical examples are provided to show the effectiveness of the main results.