Synchronization of spatiotemporal chaos in complex networks via backstepping

A backstepping approach is proposed for the synchronization of chain networks of multi-spatiotemporal chaotic systems with topologically equivalent structures.The synchronization of multi-spatiotemporal chaotic systems is implemented by adding the control only to a terminal node,and the controller is designed via a corresponding update law.The control law is applied to spatiotemporal Gray-Scott systems.Numerical results demonstrate the effectiveness and the feasibility of the proposed approach.     

Cascade adaptive control of uncertain unified chaotic systems

The chaos control of uncertain unified chaotic systems is considered. Cascade adaptive control approach with only one control input is presented to stabilize states of the uncertain unified chaotic system at the zero equilibrium point. Since an adaptive controller based on dynamic compensation mechanism is employed,the exact model of the unified chaotic system is not necessarily required. By choosing appropriate controller parameters,chaotic phenomenon can be suppressed and the response speed is tunable. Sufficient condition for the asymptotic stability of the approach is derived. Numerical simulation results confirm that the cascade adaptive control approach with only one control signal is valid in chaos control of uncertain unified chaotic systems.     

Chaos suppression of uncertain gyros in a given finite time

The gyro is one of the most interesting and everlasting nonlinear dynamical systems,which displays very rich and complex dynamics,such as sub-harmonic and chaotic behaviors.We study the chaos suppression of the chaotic gyros in a given finite time.Considering the effects of model uncertainties,external disturbances,and fully unknown parameters,we design a robust adaptive finite-time controller to suppress the chaotic vibration of the uncertain gyro as quickly as possible.Using the finite-time control technique,we give the exact value of the chaos suppression time.A mathematical theorem is presented to prove the finite-time stability of the proposed scheme.The numerical simulation shows the efficiency and usefulness of the proposed finite-time chaos suppression strategy.     

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.     

Impulsive control of chaotic systems with exogenous perturbations

The impulsive control of chaotic systems, which are subjected to unbounded exogenous perturbations, is considered. By using the theory of impulsive differential equation together with the fuzzy control technique, the authors propose an impulsive robust chaos controlling criterion expressed as linear matrix inequalities （LMIs）. Based on the proposed control criterion, the procedure for designing impulsive controllers of common （perturbed） chaotic systems is provided. Finally, a numerical example is given to demonstrate the obtained theoretical result.     

Synchronization between fractional-order chaotic systems and integer orders chaotic systems (fractional-order chaotic systems)

Based on the idea of tracking control and stability theory of fractional-order systems, a controller is designed to synchronize the fractional-order chaotic system with chaotic systems of integer orders, and synchronize the different fractional-order chaotic systems. The proposed synchronization approach in this paper shows that the synchronization between fractional-order chaotic systems and chaotic systems of integer orders can be achieved, and the synchronization between different fractional-order chaotic systems can also be realized. Numerical experiments show that the present method works very well.     

Adaptive generalized functional synchronization of chaotic systems with unknown parameters

A universal adaptive generalized functional synchronization approach to any two different or identical chaotic systems with unknown parameters is proposed, based on a unified mathematical expression of a large class of chaotic system. Self-adaptive parameter law and control law are given in the form of a theorem. The synchronization between the three-dimensional R6ssler chaotic system and the four-dimensional Chen＇s hyper-chaotic system is studied as an example for illustration. The computer simulation results demonstrate the feasibility of the method proposed.     

Bifurcation control and chaos in a linear impulsive system

Bifurcation control and the existence of chaos in a class of linear impulsive systems are discussed by means of both theoretical and numerical ways.Chaotic behaviour in the sense of Marotto’s definition is rigorously proven.A linear impulsive controller,which does not result in any change in one period-1 solution of the original system,is proposed to control and anti-control chaos.The numerical results for chaotic attractor,route leading to chaos,chaos control,and chaos anti-control,which are illustrated with two examples,are in good agreement with the theoretical analysis.     

Synchronization between two different noise-perturbed chaotic systems with unknown parameters

In this paper, a general method of synchronizing noise-perturbed chaotic systems with unknown parameters is proposed. Based on the LaSalle-type invariance principle for stochastic differential equations and by employing a combination of feedback control and adaptive control, some sufficient conditions of chaos synchronization between these noise-perturbed systems with unknown parameters are established. The model used in the research is the chaotic system, but the method is also applicable to the hyperchaotic systems. Unified system and noise-perturbed RSssler system, hyperchaotic Chen system and nolse-perturbed hyperchaotic RSssler system are taken for illustrative examples to demonstrate this technique.[第一段]     

PC synchronization of a class of chaotic systems via event-triggered control

The PC synchronization of a class of chaotic systems is investigated in this paper. The drive system is assumed to have only one state variable available. By constructing proper observers, some novel criteria for PC synchronization are proposed via event-triggered control scheme. The Lu¨ system and Chen system are taken as examples to demonstrate the efficiency of the proposed approach.     

Controlling fractional order chaotic systems based on Takagi-Sugeno fuzzy model and adaptive adjustment mechanism

In this Letter, a kind of novel model, called the generalized Takagi-Sugeno (T-S) fuzzy model, is first developed by extending the conventional T-S fuzzy model. Then, a simple but efficient method to control fractional order chaotic systems is proposed using the generalized T-S fuzzy model and adaptive adjustment mechanism (AAM). Sufficient conditions are derived to guarantee chaos control from the stability criterion of linear fractional order systems. The proposed approach offers a systematic design procedure for stabilizing a large class of fractional order chaotic systems from the literature about chaos research. The effectiveness of the approach is tested on fractional order Rössler system and fractional order Lorenz system.     

不确定混沌系统的多项式函数模型补偿控制

针对不确定混沌系统控制问题, 研究了一种基于共轭梯度法(conjugate gradient algorithm, CGA)的多项式函数模型 (polynomial-basis-functions model, PBFM)的补偿控制方法. 该方法首先用PBFM对混沌系统的动力学特性进行拟合, 然后用拟合好的PBFM模型对不确定混沌系统进行前馈补偿控制. 该方法的特点是不需要被控混沌系统的数学模型, 可以快速跟踪任意给定的参考信号. 数值仿真试验表明了该方法不仅具有响应速度快、控制精度高, 而且具有较强的抑制混沌系统参数摄动能力和抗干扰能力. 关键词： 混沌控制 多项式函数模型 共轭梯度法     

Chaos synchronization of uncertain Genesio-Tesi chaotic systems with deadzone nonlinearity

In this Letter, the concept of practical synchronization is introduced and the chaos synchronization of uncertain Genesio-Tesi chaotic systems with deadzone nonlinearity is investigated. Based on the time-domain approach, a tracking control is proposed to realize chaos synchronization for the uncertain Genesio-Tesi chaotic systems with deadzone nonlinearity. Moreover, the guaranteed exponential convergence rate and convergence radius can be pre-specified. Finally, a numerical example is provided to illustrate the feasibility and effectiveness of the obtained result.     

混沌系统的遗传神经网络控制

提出遗传神经网络控制混沌新方法.将小扰动技术和周期控制技术结合起来，用遗传算法训练神经网络，使之成为混沌控制器.对Henon映射和Logistic映射的仿真结果说明控制器能产生小扰动控制序列信号，将混沌振荡转变成规则运动状态.该方法无需了解动态系统数学模型，具有一定抗噪声干扰能力，可将它推广应用到其他混沌系统的控制中. 关键词： 遗传算法 神经网络 混沌 周期控制     

具有死区和饱和输入的自适应混沌控制

研究了一类具有死区饱和输入的不确定时滞混沌系统的跟踪问题.基于滑模控制原理，提出了一种自适应控制的新方案.该方法不仅克服了已有结果的设计缺陷，还取消了死区斜率已知和死区对称的假设，并从理论上分析证明了跟踪误差渐近收敛到零.最后，Duffing-Holme系统的仿真结果表明了该方案的有效性.     

Stability criterion for synchronization of chaotic systems using linear feedback control

This Letter introduces linear balanced feedback control scheme to design controller for the synchronization of two identical chaotic systems based on Lyapunov stability theory and constrained extreme approach. The technique is applied to synchronizing two identical four-scroll chaotic systems and guiding balanced feedback gains design. In accordance with the result of the analysis, an adaptive control scheme is proposed for chaos synchronization when the parametric variations of the response system are uncertain. The feasibility and effectiveness of the proposed synchronization scheme are verified via numerical simulations.     

A New Approach for Controlling Chaos Based on Direct Optimizing Predictive Control

We introduce the predictive control theory into the study of chaos control and propose a direct optimizing predictive control algorithm based on a neural network model. The proposed control system stabilizes the chaotic motion in an unknown chaotic system onto the desired target trajectory. Compared with the existing similar algorithms, the proposed control system has faster response, so it requires much shorter time for the stabilization of the chaotic systems.The proposed approach can control hyperchaos and the algorithm is simple. The convergence of the control algorithm and the stability of the control system can be guaranteed. The theoretic analysis and simulations demonstrate the effectiveness of the algorithm.     

Finite-time synchronization for a class of chaotic and hyperchaotic systems via adaptive feedback controller

This Letter investigates chaos synchronization of chaotic and hyperchaotic systems. Based on finite-time stability theory, a simple adaptive control method for realizing chaos synchronization in a finite time is proposed. In comparison with previous methods, the present method is not only simple, but could also be easily utilized in application. Numerical simulations are given to illustrate the effectiveness and validity of the proposed approach.     

Impulsive stabilization and synchronization of a class of chaotic delay systems

The problems of control and synchronization of a class of chaotic systems with time delay via the impulsive control approach are investigated. Based on the Lyapunov-like stability theory for impulsive functional differential equations, several sufficient conditions are derived to guarantee chaos control and synchronization. Furthermore, we address the chaos quasisynchronization in the presence of single-parameter mismatch. Several illustrated examples are also given to show the effectiveness of the proposed methods.