Finite-time robust control of uncertain fractional-order Hopfield neural networks via sliding mode control

The finite-time control of uncertain fractional-order Hopfield neural networks is investigated in this paper. A switched terminal sliding surface is proposed for a class of uncertain fractional-order Hopfield neural networks. Then a robust control law is designed to ensure the occurrence of the sliding motion for stabilization of the fractional-order Hopfield neural networks. Besides, for the unknown parameters of the fractional-order Hopfield neural networks, some estimations are made. Based on the fractional-order Lyapunov theory, the finite-time stability of the sliding surface to origin is proved well. Finally, a typical example of three-dimensional uncertain fractional-order Hopfield neural networks is employed to demonstrate the validity of the proposed method.

Adaptive fuzzy synchronization for a class of fractional-order neural networks

In this paper, synchronization for a class of uncertain fractional-order neural networks with external disturbances is discussed by means of adaptive fuzzy control. Fuzzy logic systems, whose inputs are chosen as synchronization errors, are employed to approximate the unknown nonlinear functions. Based on the fractional Lyapunov stability criterion, an adaptive fuzzy synchronization controller is designed, and the stability of the closed-loop system, the convergence of the synchronization error, as well as the boundedness of all signals involved can be guaranteed. To update the fuzzy parameters, fractional-order adaptations laws are proposed. Just like the stability analysis in integer-order systems, a quadratic Lyapunov function is used in this paper. Finally, simulation examples are given to show the effectiveness of the proposed method.

Coexistence and local Mittag–Leffler stability of fractional-order recurrent neural networks with discontinuous activation functions

In this paper, coexistence and local Mittag–Leffler stability of fractional-order recurrent neural networks with discontinuous activation functions are addressed. Because of the discontinuity of the activation function, Filippov solution of the neural network is defined. Based on Brouwer's fixed point theorem and definition of Mittag–Leffler stability, sufficient criteria are established to ensure the existence of (2k + 3)~n (k ≥ 1) equilibrium points, among which (k + 2)~n equilibrium points are locally Mittag–Leffler stable. Compared with the existing results, the derived results cover local Mittag–Leffler stability of both fractional-order and integral-order recurrent neural networks. Meanwhile discontinuous networks might have higher storage capacity than the continuous ones. Two numerical examples are elaborated to substantiate the effective of the theoretical results.

Multiple Lagrange stability and Lyapunov asymptotical stability of delayed fractional-order Cohen-Grossberg neural networks

This paper addresses the coexistence and local stability of multiple equilibrium points for fractional-order Cohen-Grossberg neural networks(FOCGNNs)with time delays.Based on Brouwer's fixed point theorem,sufficient conditions are established to ensure the existence of Πi=1^n(2Ki+1)equilibrium points for FOCGNNs.Through the use of Hardy inequality,fractional Halanay inequality,and Lyapunov theory,some criteria are established to ensure the local Lagrange stability and the local Lyapunov asymptotical stability of Πi=1^n(Ki+1)equilibrium points for FOCGNNs.The obtained results encompass those of integer-order Hopfield neural networks with or without delay as special cases.The activation functions are nonlinear and nonmonotonic.There could be many corner points in this general class of activation functions.The structure of activation functions makes FOCGNNs could have a lot of stable equilibrium points.Coexistence of multiple stable equilibrium points is necessary when neural networks come to pattern recognition and associative memories.Finally,two numerical examples are provided to illustrate the effectiveness of the obtained results.

Finite-time Mittag-Leffler synchronization of fractional-order delayed memristive neural networks with parameters uncertainty and discontinuous activation functions

The finite-time Mittag-Leffler synchronization is investigated for fractional-order delayed memristive neural networks(FDMNN)with parameters uncertainty and discontinuous activation functions.The relevant results are obtained under the framework of Filippov for such systems.Firstly,the novel feedback controller,which includes the discontinuous functions and time delays,is proposed to investigate such systems.Secondly,the conditions on finite-time Mittag-Leffler synchronization of FDMNN are established according to the properties of fractional-order calculus and inequality analysis technique.At the same time,the upper bound of the settling time for Mittag-Leffler synchronization is accurately estimated.In addition,by selecting the appropriate parameters of the designed controller and utilizing the comparison theorem for fractional-order systems,the global asymptotic synchronization is achieved as a corollary.Finally,a numerical example is given to indicate the correctness of the obtained conclusions.

Finite-time Mittag-Leffler synchronization of fractional-order complex-valued memristive neural networks with time delay

Without dividing the complex-valued systems into two real-valued ones, a class of fractional-order complex-valued memristive neural networks(FCVMNNs) with time delay is investigated. Firstly, based on the complex-valued sign function, a novel complex-valued feedback controller is devised to research such systems. Under the framework of Filippov solution, differential inclusion theory and Lyapunov stability theorem, the finite-time Mittag-Leffler synchronization(FTMLS) of FCVMNNs with time delay can be realized. Meanwhile, the upper bound of the synchronization settling time(SST) is less conservative than previous results. In addition, by adjusting controller parameters, the global asymptotic synchronization of FCVMNNs with time delay can also be realized, which improves and enrich some existing results. Lastly,some simulation examples are designed to verify the validity of conclusions.

Dynamic Analysis of Fractional-Order Fuzzy BAM Neural Networks with Delays in the Leakage Terms

In this paper, based on the theory of fractional-order calculus, we obtain some sufficient conditions for the uniform stability of fractional-order fuzzy BAM neural networks with delays in the leakage terms. Moreover, the existence, uniqueness and stability of its equilibrium point are also proved. A numerical example is presented to demonstrate the validity and feasibility of the proposed results.

Dynamic Analysis of Some Impulsive Fractional-Order Neural Network with Mixed Delay

In this paper,the authors study some impulsive fractionalorder neural network with mixed delay. By the fractional integral and the definition of stability, the existence of solutions of the network is proved,and the sufficient conditions for stability of the system are presented. Some examples are given to illustrate the main results.

Intelligent Networks for Chaotic Fractional-Order Nonlinear Financial Model

The purpose of this paper is to present a numerical approach based on the artificial neural networks(ANNs)for solving a novel fractional chaotic financial model that represents the effect of memory and chaos in the presented system.The method is constructed with the combination of the ANNs along with the Levenberg-Marquardt backpropagation(LMB),named the ANNs-LMB.This technique is tested for solving the novel problem for three cases of the fractional-order values and the obtained results are compared with the reference solution.Fifteen numbers neurons have been used to solve the fractional-order chaotic financial model.The selection of the data to solve the fractional-order chaotic financial model are selected as 75%for training,10%for testing,and 15%for certification.The results indicate that the presented approximate solutions fit exactly with the reference solution and the method is effective and precise.The obtained results are testified to reduce the mean square error(MSE)for solving the fractional model and verified through the various measures including correlation,MSE,regression histogram of the errors,and state transition(ST).

Existence and Stability Analysis of Fractional Order BAM Neural Networks with a Time Delay

Based on the theory of fractional calculus, the contraction mapping principle, Krasnoselskii fixed point theorem and the inequality technique, a class of Caputo fractional-order BAM neural networks with delays in the leakage terms is investigated in this paper. Some new sufficient conditions are established to guarantee the existence and uniqueness of the nontrivial solution. Moreover, uniform stability of such networks is proposed in fixed time intervals. Finally, an illustrative example is also given to demonstrate the effectiveness of the obtained results.

An Image Encryption Algorithm Based on BP Neural Network and Hyperchaotic System

To reduce the bandwidth and storage resources of image information in communication transmission, and improve the secure communication of information. In this paper, an image compression and encryption algorithm based on fractional-order memristive hyperchaotic system and BP neural network is proposed. In this algorithm, the image pixel values are compressed by BP neural network, the chaotic sequences of the fractional-order memristive hyperchaotic system are used to diffuse the pixel values. The experimental simulation results indicate that the proposed algorithm not only can effectively compress and encrypt image, but also have better security features. Therefore, this work provides theoretical guidance and experimental basis for the safe transmission and storage of image information in practical communication.

Fractional Order Nonlinear Bone Remodeling Dynamics Using the Supervised Neural Network

This study aims to solve the nonlinear fractional-order mathematical model(FOMM)by using the normal and dysregulated bone remodeling of themyeloma bone disease(MBD).For themore precise performance of the model,fractional-order derivatives have been used to solve the disease model numerically.The FOMM is preliminarily designed to focus on the critical interactions between bone resorption or osteoclasts(OC)and bone formation or osteoblasts(OB).The connections of OC and OB are represented by a nonlinear differential system based on the cellular components,which depict stable fluctuation in the usual bone case and unstable fluctuation through the MBD.Untreated myeloma causes by increasing the OC and reducing the osteoblasts,resulting in net bone waste the tumor growth.The solutions of the FOMM will be provided by using the stochastic framework based on the Levenberg-Marquardt backpropagation(LVMBP)neural networks(NN),i.e.,LVMBPNN.The mathematical performances of three variations of the fractional-order derivative based on the nonlinear disease model using the LVMPNN.The static structural performances are 82%for investigation and 9%for both learning and certification.The performances of the LVMBPNN are authenticated by using the results of the Adams-Bashforth-Moulton mechanism.To accomplish the capability,steadiness,accuracy,and ability of the LVMBPNN,the performances of the error histograms(EHs),mean square error(MSE),recurrence,and state transitions(STs)will be provided.

Mittag-Leffler stability analysis of multiple equilibrium points in impulsive fractional-order quaternion-valued neural networks

In this study,we investigate the problem of multiple Mittag-Leffler stability analysis for fractional-order quaternion-valued neural networks(QVNNs)with impulses.Using the geometrical properties of activation functions and the Lipschitz condition,the existence of the equilibrium points is analyzed.In addition,the global Mittag-Leffler stability of multiple equilibrium points for the impulsive fractional-order QVNNs is investigated by employing the Lyapunov direct method.Finally,simulation is performed to illustrate the effectiveness and validity of the main results obtained.

Finite-Time Stability of Fractional-Order Neural Networks with Delay

Finite-time stability of a class of fractional-order neural networks is investigated in this paper. By Laplace transform, the generalized Gronwa11 inequality and estimates of Mittag-Leffier functions, sufficient conditions are pre- sented to ensure the finite-time stability of such neural models with the Caputo fractionM derivatives. Furthermore, results about asymptotical stability of fractional-order neural models are also obtained.

Dynamics analysis of fractional-order Hopfield neural networks

This paper proposes fractional-order systems for Hopfield Neural Network(HNN).The so-called Predictor Corrector Adams Bashforth Moulton Method(PCABMM)has been implemented for solving such systems.Graphical comparisons between the PCABMM and the Runge-Kutla Method(RKM)solutions for the classical HNN reveal that the proposed technique is one of the powerful tools for handling these systems.To determine all Lyapunov exponents for them,the Benettin-Wolf algorithm has been involved in the PCABMM.leased on such algorithm,the Lyapunov exponents as a function of a given parameter and as another function of the fractional-order have been described,the intermittent chaos for these systems has been explored.A new result related to the Mittag-Leffler stability of some nonlinear Fractional-order Hopfield Neural Network(FoHNN)systems has been shown.Besides,the description and the dynamic analysis of those phenomena have been discussed and verified theoretically and numerically via illustrating the phase portraits and the Lyapunov exponents'diagrams.

A novel color image encryption algorithm based on a fractional-order discrete chaotic neural network and DNA sequence operations

A novel color image encryption algorithm based on dynamic deoxyribonucleic acid(DNA)encoding and chaos is presented.A three-neuron fractional-order discrete Hopfield neural network(FODHNN)is employed as a pseudo-random chaotic sequence generator.Its initial value is obtained with the secret key generated by a fiveparameter external key and a hash code of the plain image.The external key includes both the FODHNN discrete step size and order.The hash is computed with the SHA-2 function.This ensures a large secret key space and improves the algorithm sensitivity to the plain image.Furthermore,a new three-dimensional projection confusion method is proposed to scramble the pixels among red,green,and blue color components.DNA encoding and diffusion are used to diffuse the image information.Pseudo-random sequences generated by FODHNN are employed to determine the encoding rules for each pixel and to ensure the diversity of the encoding methods.Finally,confusion II and XOR are used to ensure the security of the encryption.Experimental results and the security analysis show that the proposed algorithm has better performance than those reported in the literature and can resist typical attacks.

Mixed H_∞ and Passive Projective Synchronization for Fractional Order Memristor-Based Neural Networks with Time-Delay and Parameter Uncertainty

This paper investigates the mixed Ho~ and passive projective synchronization problem for fractional-order （FO） memristor-based neural networks. Our aim is to design a controller such that, though the unavoidable phenomena of time-delay and parameter uncertainty are fully considered, the resulting closed-loop system is asymptotically stable with a mixed H∞ and passive performance level. By combining active and adaptive control methods, a novel hybrid control strategy is designed, which can guarantee the robust stability of the closed-loop system and also ensure a mixed H∞ and passive performance level. Via the application of FO Lyapunov stability theory, the projective synchronization conditions are addressed in terms of linear matrix inequaiity techniques. Finally, two simulation examples are given to illustrate the effectiveness of the proposed method.

舰载相控阵雷达光束指向控制策略研究

为改善在舰载相控阵雷达的光束控制中指向精度的参数指标,同时增强光束控制器性能与舰载相控阵雷达检测的准确性,本文通过相关影响因素分析,选取合理的器件参数,期望达到最佳效果。然后研究基于分数阶耦合复值神经网络的光束指向控制策略,通过对分数阶复值神经网络的投影同步的研究证明,系统的投影同步可以控制光束的指向。采用哈里斯鹰算法(HHO)对液晶相控阵进行光束指向精度优化,仿真实验结果表明,本文设计的全局与局部并行优化策略的哈里斯鹰算法,归一化精度误差由100数量级优化为10-4数量级,有效提高了舰载相控阵雷达的检测精度。

Distributed event-triggered formation control of UGV-UAV heterogeneous multi-agent systems for ground-air cooperation

Within the context of ground-air cooperation,the distributed formation trajectory tracking control problems for the Heterogeneous Multi-Agent Systems(HMASs)is studied.First,considering external disturbances and model uncertainties,a graph theory-based formation control protocol is designed for the HMASs consisting of Unmanned Aerial Vehicles(UAVs)and Unmanned Ground Vehicles(UGVs).Subsequently,a formation trajectory tracking control strategy employing adaptive Fractional-Order Sliding Mode Control(FOSMC)method is developed,and a Feedback Multilayer Fuzzy Neural Network(FMFNN)is introduced to estimate the lumped uncertainties.This approach empowers HMASs to adaptively follow the expected trajectory and adopt the designated formation configuration,even in the presence of various uncertainties.Additionally,an event-triggered mechanism is incorporated into the controller to reduce the update frequency of the controller and minimize the communication exchange among the agents,and the absence of Zeno behavior is rigorously demonstrated by an integral inequality analysis.Finally,to confirm the effectiveness of the proposed formation control protocol,some numerical simulations are presented.