Adaptive neural output feedback control of nonlinear discrete-time systems

In this paper, a nonautonomous impulsive neutral-type neural network with delays is considered. By establishing a singular impulsive delay differential inequality and employing contraction mapping principle, several sufficient conditions ensuring the existence and global exponential stability of the periodic solution for the impulsive neutral-type neural network with delays are obtained. Our results can extend and improve earlier publications. An example is given to illustrate the theory.     

Globally exponential stability of stochastic neutral-type delayed neural networks with impulsive perturbations and Markovian switching

The problem of globally exponential stability of stochastic neutral-type delayed neural networks with impulsive perturbations and Markovian switching is studied in this paper. By using the Lyapunov?CKrasovskii method and the stochastic analysis approach, a sufficient condition to ensure globally exponential stability for the stochastic neutral-type delayed neural networks with impulsive perturbations and Markovian switching is derived. Finally, a numerical example is given to illustrate the effectiveness of the result proposed in this paper.     

Global Mittag-Leffler stability and synchronization of impulsive fractional-order neural networks with time-varying delays

In this paper we consider a class of impulsive Caputo fractional-order cellular neural networks with time-varying delays. Applying the fractional Lyapunov method and Mittag-Leffler functions, we give sufficient conditions for global Mittag-Leffler stability which implies global asymptotic stability of the network equilibrium. Our results provide a design method of impulsive control law which globally asymptotically stabilizes the impulse free fractional-order neural network time-delay model. The synchronization of fractional chaotic networks via non-impulsive linear controller is also considered. Illustrative examples are given to demonstrate the effectiveness of the obtained results.     

Input-to-state stability of impulsive reaction–diffusion neural networks with infinite distributed delays

In this paper, we focus on the global existence–uniqueness and input-to-state stability of the mild solution of impulsive reaction–diffusion neural networks with infinite distributed delays. First, the model of the impulsive reaction–diffusion neural networks with infinite distributed delays is reformulated in terms of an abstract impulsive functional differential equation in Hilbert space and the local existence–uniqueness of the mild solution on impulsive time interval is proven by the Picard sequence and semigroup theory. Then, the diffusion–dependent conditions for the global existence–uniqueness and input-to-state stability are established by the vector Lyapunov function and M-matrix where the infinite distributed delays are handled by a novel vector inequality. It shows that the ISS properties can be retained for the destabilizing impulses if there are no too short intervals between the impulses. Finally, three numerical examples verify the effectiveness of the theoretical results and that the reaction–diffusion benefits the input-to-state stability of the neural-network system.

     

Different impulsive effects on synchronization of fractional-order memristive BAM neural networks

This paper considered exponential synchronization in fractional-order memristive BAM neural networks (FMBAMNNs) with time delay via switching jumps mismatch. Exponential function is introduced for studying fractional-order differential system. According to double-layer structure of FMBAMNNs, two controllers are designed for the response FMBAMNNs. Particularly, more wide ranges of impulsive effects, which are affected by fractional-order \(\alpha \), are discussed in detail. One case is that the impulsive effect contributes to system convergence, and the other is that the impulsive effect destroys the system convergence. Based on the fractional stability theory and the definition of average impulsive interval, several criteria for achieving synchronization of FMBAMNNs are established. For different impulsive effects, the rate of convergence is precisely expressed. Finally, numerical examples verify the validity of the theoretical results.     

Sampled-data-based lag synchronization of chaotic delayed neural networks with impulsive control

Nonlinear Dynamics - In the framework of sampled-data control, this paper deals with the lag synchronization of chaotic neural networks with time delay meanwhile taking the impulsive control into...     

Impulsive pinning complex dynamical networks and applications to firing neuronal synchronization

The primary objective of this paper is to propose a new approach for analyzing pinning stability in a complex dynamical network via impulsive control. A?simple yet generic criterion of impulsive pinning synchronization for such coupled oscillator network is derived analytically. It is shown that a single impulsive controller can always pin a given complex dynamical network to a homogeneous solution. Subsequently, the theoretic result is applied to a small-world (SW) neuronal network comprised of the Hindmarsh?CRose oscillators. It turns out that the firing activities of a single neuron can induce synchronization of the underlying neuronal networks. This conclusion is obviously in consistence with empirical evidence from the biological experiments, which plays a significant role in neural signal encoding and transduction of information processing for neuronal activity. Finally, simulations are provided to demonstrate the practical nature of the theoretical results.     

Function projective synchronization of impulsive neural networks with mixed time-varying delays

In this paper, the exponential function projective synchronization of impulsive neural networks with mixed time-varying delays is investigated. Based on the contradiction method and analysis technique, some novel criteria are obtained to guarantee the function projective synchronization of considered networks via combining open-loop control and linear feedback control. As some special cases, several control strategies are given to ensure the realization of complete synchronization, anti-synchronization, and the stabilization of the addressed neural networks. Finally, two examples and their numerical simulations are given to show the effectiveness and feasibility of the proposed synchronization schemes.     

负反馈诱发神经电振荡的反常现象的复杂动力学

传统观念认为,负反馈容易使系统达到稳定平衡点而正反馈容易引起振荡.本研究基于神经元理论模型,提出了负反馈可以诱发稳定平衡点、也就是静息、变为振荡、也就是放电的新观点.在Hopf分岔点附近,作用在静息上的一次足够大的负向脉冲电流的抑制性刺激,能够引起一个动作电位及随后的衰减振荡的后电位;而能够在后电位上诱发出动作电位的负脉冲电流强度阈值也是衰减振荡的.在模型中,引入具有时滞($\tau$)的负反馈来模拟抑制性自突触,一个动作电位诱发的负反馈自突触电流会作用到比动作电位延迟$\tau$的后电位上.随时滞增加,能够诱发出放电的负反馈增益强度阈值呈现出具有衰减振荡特点的类似多重相干共振的特性,衰减振荡的周期与电流阈值曲线的周期以及分岔点附近的放电周期相关.另外,负反馈还能诱发出放电与静息共存的复杂行为.本研究的结果不仅揭示了负反馈的新的反常调控作用,还有助于理解在现实神经系统中存在的慢抑制性自突触的潜在功能.      

IMPULSIVE CONTROL FOR THE STABILIZATION AND SYNCHRONIZATION OF LUR'E SYSTEMS

IntroductionInpractice ,thereexistmanyexamplesofimpulsivecontrolsystems (seeRefs.[1 ,2 ,3 ] ) .Recently ,impulsivecontrolhasbeenwidelyusedtostabilizeandsynchronizechaoticsystems(seeRefs.[4～ 1 5] ) .Forexample,thepredictivePoincarecontrol[4 ]andtheoccasionalproportionalfeedbackcontrol[5 ]aretwoimpulsivecontrolschemeswithvaryingimpulsiveintervals.Yangetal.inRefs.[7,1 1 ]studied ,respectively ,thestabilizationandsynchronizationofaclassofchaoticsystemscalledLorenzsystems .YangandChuainRef.[1 …     

On impulsive processes

Consider impulsive processes that consists of between two impulses non-autonomous, non-linear continuous processes subjected to time-varying impulsive constraints. By extending compact processes defined by Dafermos for non-autonomous systems without impulses, a class of regular impulsive processes is provided and its applications are stressed by selected examples. A weak invariance principle and an invariance principle are established for the regular impulsive processes. The paper thus lays ground work for geometric theory of general impulsive processes.     

Finite-time consensus of nonlinear multi-agent systems via impulsive time window theory: a two-stage control strategy

This paper concentrates on the finite-time consensus problem faced by nonlinear multi-agent systems (MASs) via impulsive time window theory with a two-stage control (TSC) strategy. The TSC strategy divides the whole control period into two parts: a variable impulsive control stage and a finite-time consensus control stage. Different from general single-stage control, TSC can dynamically adjust the time periods of impulsive control and finite-time control according to practical application requirements. Variable impulsive control is also discussed in this paper. Compared with the sampling based on traditional fixed impulsive theory, impulsive sampling in the TSC strategy occurs randomly within an impulsive time window and provides much more flexibility. In addition, a switching topology scheme is introduced in this paper to strengthen the stability of MASs. Finally, two numerical simulation examples (one leaderless case and one leader-following case) are used for the theoretical analysis.

     

Reliable impulsive lag synchronization for a class of nonlinear discrete chaotic systems

The problem of reliable impulsive lag synchronization for a class of nonlinear discrete chaotic systems is investigated in this paper. Firstly a reliable impulsive controller is designed by the impulsive control theory. Then, some sufficient conditions for reliable impulsive lag synchronization between the drive system and the response system are obtained. Numerical simulations are given to show the effectiveness of the proposed method.     

IMPULSIVE CONTROL FOR THE STABILIZATION AND SYNCHRONIZATION OF LUR＇ E SYSTEMS

An impulsive control scheme of the Lur‘e system and several theorems on stability of impulsive control systems was presented, these theorems were then used to find the conditions under which the Lur‘e system can be stabilized by using impulsive control with varying impulsive intervals. The parameters of Lur‘e system and impulsive control law are given, a theory of impulsive synchronization of two Lur‘e system is also presented. A numerical example is used to verify the theoretical result.     

Nonlinear observer-based impulsive synchronization in chaotic systems with multiple attractors

The issue of impulsive synchronization of the coupled Newton–Leipnik system is investigated. Based on the impulsive stability theory, nonlinear observer-based impulsive synchronization scheme is derived. A new and less conservative criteria for impulsive synchronization via nonlinear observer is proposed. The boundary of the stable regions is also estimated. One important advantage of the proposed method is that it is also applicable for the systems with more than one attractor. Numerical simulations on Newton–Leipnik system are illustrated to verify the theoretical results.     

Rucklidge系统的脉冲控制

应用脉冲控制的基本思想和李雅普诺夫（Lyapunov）函数方法Rucklidge系统进行混沌控制，提出了指数稳定和非线性脉冲系统的渐进稳定的一般准则来保证脉冲控制是全局渐进稳定的。理论证明和数值模拟均表明所提出的脉冲准则是有效的．脉冲控制Rucklidge系统的平凡解是全局指数稳定的。     

Synchronization of chaotic systems using fuzzy impulsive control

This paper investigates the problem of fuzzy impulsive control to synchronize two chaotic systems using a novel time-dependent Lyapunov function approach. Compared with the existing time-independent Lyapunov methods, the proposed method enables us to exploit more information on the impulsive intervals. Initially, using the Lyapunov technique and two parameterized linear matrix inequality (LMI) techniques, some less conservative synchronization criteria via a fuzzy impulsive controller using the states of both drive and response chaotic systems are derived. Subsequently, an LMI approach to designing such a fuzzy impulsive controller is developed to realize the synchronization. Finally, the proposed method is applied to the chaotic Lorenz system and Rösler system to illustrate its effectiveness.     

Impulsive control induced effects on dynamics of single and coupled ODE systems

The dynamics of differential system can be changed very obviously after inputting impulse signals. Previous studies show that the single chaotic system can be controlled to periodic motions using impulsive control method. It was well known that the dynamics of hyper-chaotic and coupled systems are very important and more complex than those of a single system. In this paper, particular impulsive control of the hyper-chaotic Lü system was proposed, which is with outer impulsive signals. It can be seen that such impulsive strategy can generate chaos from periodic orbit or control chaos to periodic orbit etc. For the first time, impulsive control induced effects on dynamics of coupled systems are considered in this paper, where the impulse effect has outer input signals. Many interesting and useful results are obtained. The coupled system can realize synchronization and its synchronization manifold can be changed with such impulsive control signals. Strict theories are given, and numerical simulations confirm the correctness of theoretical results.     

Adaptive impulsive synchronization of uncertain drive-response complex-variable chaotic systems

In this paper, impulsive synchronization of drive-response complex-variable chaotic systems is investigated. The drive-response systems with known parameters is considered via impulsive control and adaptive scheme as well as systems with unknown parameters. Noticeably, adaptive strategy is adopted to relax the restriction on the impulsive interval, and the system parameters need not to be known beforehand. According to the Lyapunov stability theory, some synchronization criteria are derived and verified by several numerical simulations.     

Chemical chaos in enzyme kinetics

In this paper, the effect of impulsive perturbation on enzyme kinetics is investigated. The impulsive perturbation is affected by introducing periodic constant input. The dynamical behavior of system is simulated and bifurcation diagrams are obtained. The results show that impulsive perturbation can easily give rise to complex dynamics, which includes: quasi-periodic oscillation, periodic doubling cascade, periodic halving cascade, attractor crisis and chaotic bands with periodic windows.