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 Gronwall inequality and estimates of Mittag-Leffler functions, sufficient conditions are presented to ensure the finite-time stability of such neural models with the Caputo fractional derivatives. Furthermore, results about asymptotical stability of fractional-order neural models are also obtained.     

Adaptive synchronization of a class of fractional-order complex-valued chaotic neural network with time-delay

This paper is concerned with the adaptive synchronization of fractional-order complex-valued chaotic neural networks (FOCVCNNs) with time-delay. The chaotic behaviors of a class of fractional-order complex-valued neural network are investigated. Meanwhile, based on the complex-valued inequalities of fractional-order derivatives and the stability theory of fractional-order complex-valued systems, a new adaptive controller and new complex-valued update laws are proposed to construct a synchronization control model for fractional-order complex-valued chaotic neural networks. Finally, the numerical simulation results are presented to illustrate the effectiveness of the developed synchronization scheme.     

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.     

Stability and synchronization of fractional-order complex-valued neural networks with time delay: LMI approach

In this paper, we investigate the problem of stability and synchronization of fractional-order complex-valued neural networks with time delay. By using Lyapunov–Krasovskii functional approach, some linear matrix inequality (LMI) conditions are proposed to ensure that the equilibrium point of the addressed neural networks is globally Mittag–Leffler stable. Moreover, some sufficient conditions for projective synchronization of considered fractional-order complex-valued neural networks are derived in terms of LMIs. Finally, two numerical examples are given to demonstrate the effectiveness of our theoretical results.     

Finite-time stability and synchronization for memristor-based fractional-order Cohen-Grossberg neural network

In this paper, we study the finite-time stability and synchronization problem of a classof memristor-based fractional-order Cohen-Grossberg neural network (MFCGNN) with thefractional order α ∈ (0,1]. We utilize the set-valued map and Filippov differential inclusion totreat MFCGNN because it has discontinuous right-hand sides. By using the definition ofCaputo fractional-order derivative, the definitions of finite-time stability andsynchronization, Gronwall’s inequality and linear feedback controller, two new sufficientconditions are derived to ensure the finite-time stability of our proposed MFCGNN andachieve the finite-time synchronization of drive-response systems which are constituted byMFCGNNs. Finally, two numerical simulations are presented to verify the rightness of ourproposed theorems.     

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.     

不确定分数阶时滞混沌系统自适应神经网络同步控制

针对带有完全未知的非线性不确定项和外界扰动的异结构分数阶时滞混沌系统的同步问题,基于Lyapunov稳定性理论,设计了自适应径向基函数(radial basis function,RBF)神经网络控制器以及整数阶的参数自适应律.该控制器结合了RBF神经网络和自适应控制技术,RBF神经网络用来逼近未知非线性函数,自适应律用于调整控制器中相应的参数.构造平方Lyapunov函数进行稳定性分析,基于Barbalat引理证明了同步误差渐近趋于零.数值仿真结果表明了该控制器的有效性.     

基于滑模控制实现分数阶混沌系统的投影同步

针对分数阶混沌系统的投影同步问题,提出了一种基于主动滑模原理的控制器.基于分数阶线性系统的稳定性理论,分析了该方法的稳定性.分别以同结构分数阶Liu-Liu系统的投影同步和异结构分数阶Chen-Liu系统的投影同步为例进行了数值仿真,仿真结果验证了主动滑模控制方法在分数阶混沌系统投影同步中的有效性. 关键词： 分数阶混沌系统 滑模控制 投影同步     

分数阶van der Pol振子的超谐共振

以含分数阶微分项的van der Pol振子为对象,研究其超谐共振时的动力学特性.首先,通过平均法得到了系统的一阶近似解,提出了超谐共振时等效线性阻尼和等效线性刚度的概念,研究了分数阶微分项的系数和阶次以等效线性阻尼和等效线性刚度的形式对系统动力学特性的影响.随后,建立了超谐共振时定常解的幅频曲线的解析表达式,得到了超谐共振周期响应的稳定性判断准则并提出等效非线性阻尼和非线性稳定性条件参数的概念.最后,通过数值仿真比较了分数阶与整数阶系统的幅频曲线,分析了分数阶微分项的系数和阶次对响应幅值、幅频曲线以及系统稳定性的影响.     

No-chattering sliding mode control in a class of fractional-order chaotic systems

A no-chattering sliding mode control strategy for a class of fractional-order chaotic systems is proposed in this paper. First, the sliding mode control law is derived to stabilize the states of the commensurate fractional-order chaotic system and the non-commensurate fractional-order chaotic system, respectively. The designed control scheme guarantees the asymptotical stability of an uncertain fractional-order chaotic system. Simulation results are given for several fractional-order chaotic examples to illustrate the effectiveness of the proposed scheme.     

Synchronization of uncertain fractional-order chaotic systems via a novel adaptive controller

This paper deals with the drive-response synchronization scheme for uncertain fractional-order chaotic systems. Some novel sufficient conditions for chaos synchronization of fractional-order chaotic systems with model uncertainties and external disturbances are derived by using the fractional-order extension of the Lyapunov stability theorem. The designed synchronization are new, simple and yet easily realized experimentally compared with those where complex control functions are used. Simulation results are given for several fractional-order chaotic examples to illustrate the effectiveness of the proposed scheme.     

Adaptive control and synchronization of a fractional-order chaotic system

In this paper, the chaotic dynamics of a three-dimensional fractional-order chaotic system is investigated. The lowest order for exhibiting chaos in the fractional-order system is obtained. Adaptive schemes are proposed for control and synchronization of the fractional-order chaotic system based on the stability theory of fractional-order dynamic systems. The presented schemes, which contain only a single-state variable, are simple and flexible. Numerical simulations are used to demonstrate the feasibility of the presented methods.     

Dynamic analysis of the fractional-order Liu system and its synchronization

Based on the stability theory of fractional-order systems, the dynamic behaviors of fractional-order Liu system are studied theoretically. Coupling synchronization of two identical fractional-order chaotic systems is also studied and a simple criterion is presented. Numerical simulations show the effectiveness of our methods.     

Linear matrix inequality criteria for robust synchronization of uncertain fractional-order chaotic systems

This paper is devoted to synchronization of uncertain fractional-order chaotic systems with fractional-order α: 0?相似文献   

Function projective synchronization between fractional-order chaotic systems and integer-order chaotic systems

This paper investigates the function projective synchronization between fractional-order chaotic systems and integer-order chaotic systems using the stability theory of fractional-order systems. The function projective synchronization between three-dimensional (3D) integer-order Lorenz chaotic system and 3D fractional-order Chen chaotic system are presented to demonstrate the effectiveness of the proposed scheme.     

Q-S synchronization of the fractional-order unified system

Concept of Q-S synchronization for fractional-order systems is introduced and Q-S synchronization of the fractional-order unified system is investigated in this paper. On the basis of the stability theory of the fractional-order system, two suitable control schemes are designed to achieve Q-S synchronization of the fractional-order unified systems under the given observable variables of drive system and the response system. Theoretical analysis and numerical simulations are shown to demonstrate the validity and feasibility of the proposed method.     

一个分数阶新超混沌系统的同步

研究了分数阶混沌系统的同步问题,以分数阶新超混沌系统为例,设计了三种同步方法,运用拉普拉斯变换理论和分数阶线性稳定理论给以证明,数值仿真或电路仿真证实了所提同步方法的有效性和可行性. 关键词： 分数阶 混沌同步 新超混沌系统     

Lag projective synchronization in fractional-order chaotic (hyperchaotic) systems

In this Letter, a new lag projective synchronization for fractional-order chaotic (hyperchaotic) systems is proposed, which includes complete synchronization, anti-synchronization, lag synchronization, generalized projective synchronization. It is shown that the slave system synchronizes the past state of the driver up to a scaling factor. A suitable controller for achieving the lag projective synchronization is designed based on the stability theory of linear fractional-order systems and the pole placement technique. Two examples are given to illustrate effectiveness of the scheme, in which the lag projective synchronizations between fractional-order chaotic Rössler system and fractional-order chaotic Lü system, between fractional-order hyperchaotic Lorenz system and fractional-order hyperchaotic Chen system, respectively, are successfully achieved. Corresponding numerical simulations are also given to verify the analytical results.     

Multiswitching compound–compound synchronisation of six chaotic systems

In this paper, multiswitching combination synchronisation (MSCS) scheme has been investigated in a class of three non-identical fractional-order chaotic systems. The fractional-order Lorenz and Chen systems are taken as the drive systems. The combination of multidrive systems is then synchronised with the fractional-order Lü chaotic system. In MSCS, the state variables of the two drive systems synchronise with different state variables of the response system, simultaneously. Based on the stability of fractional-order chaotic systems, the MSCS of three fractional-order non-identical systems has been investigated. For the synchronisation of three non-identical fractional-order chaotic systems, suitable controllers have been designed. Theoretical analysis and numerical results are presented to demonstrate the validity and feasibility of the applied method.     

Modified adaptive controller for synchronization of incommensurate fractional-order chaotic systems

We investigate the synchronization of a class of incommensurate fractional-order chaotic systems,and propose a modified adaptive controller for fractional-order chaos synchronization based on the Lyapunov stability theory,the fractional order differential inequality,and the adaptive strategy.This synchronization approach is simple,universal,and theoretically rigorous.It enables the synchronization of0 fractional-order chaotic systems to be achieved in a systematic way.The simulation results for the fractional-order Qi chaotic system and the four-wing hyperchaotic system are provided to illustrate the effectiveness of the proposed scheme.