Chaotic Synchronization of the Master Slave Chaotic Systems with Different Structures Based on BANG-BANG Control Principle

We propose a Bang-Bang control scheme that can synchronize master-slave chaotic systems. The chaotic systems considered here are structurally different from each other. Different from some control strategies reported previously, the scheme proposed here can be taken as a general one that is independent of the chaotic system itself.     

Control of fractional chaotic and hyperchaotic systems based on a fractional order controller

We present a new fractional-order controller based on the Lyapunov stability theory and propose a control method which can control fractional chaotic and hyperchaotic systems whether systems are commensurate or incommensurate.The proposed control method is universal, simple, and theoretically rigorous. Numerical simulations are given for several fractional chaotic and hyperchaotic systems to verify the effectiveness and the universality of the proposed control method.     

Fuzzy Modeling and Impulsive Control of a Memristor-Based Chaotic System

We mainly investigate the issues of fuzzy modeling and impulsive control of a memristor-based chaotic system and present a memristor-based chaotic system as the Takagi-Sugeno model-based fuzzy system. Then, based on the impulsive control theory of dynamical systems, a criterion ensuring impulsive stabilization of the memristorbased chaotic system is derived for the first time. An illustrative example is given to verify the effectiveness of the control scheme.     

Impulsive Control for Fractional-Order Chaotic Systems

We propose an impulsive control scheme for fractional-order chaotic systems. Based on the Takagi-Sugeno （T-S） fuzzy model and linear matrix inequalities （LMfs）, some sufficient conditions are given to stabilize the fractional-order chaotic system via impulsive control. Numerical simulation shows the effectiveness of this approach.     

Control of fractional chaotic system based on fractional-order resistor—capacitor filter

We present a new fractional-order resistor-capacitor controller and a novel control method based on the fractional-order controller to control an arbitrary three-dimensional fractional chaotic system. The proposed control method is simple, robust, and theoretically rigorous, and its anti-noise performance is satisfactory. Numerical simulations are given for several fractional chaotic systems to verify the effectiveness and the universality of the proposed control method.     

A new approach of optimal control for a class of continuous-time chaotic systems by an online ADP algorithm

We develop an online adaptive dynamic programming （ADP） based optimal control scheme for continuous-time chaotic systems. The idea is to use the ADP algorithm to obtain the optimal control input that makes the performance index function reach an optimum. The expression of the performance index function for the chaotic system is first presented. The online ADP algorithm is presented to achieve optimal control. In the ADP structure, neural networks are used to construct a critic network and an action network, which can obtain an approximate performance index function and the control input, respectively. It is proven that the critic parameter error dynamics and the closed-loop chaotic systems are uniformly ultimately bounded exponentially. Our simulation results illustrate the performance of the established optimal control method.     

Control of a fractional chaotic system based on a fractional-order resistor-capacitor filter

We present a new fractional-order resistor-capacitor controller and a novel control method based on the fractional- order controller to control an arbitrary three-dimensional fractional chaotic system. The proposed control method is simple, robust, and theoretically rigorous, and its anti-noise performance is satisfactory. Numerical simulations are given for several fractional chaotic systems to verify the effectiveness and the universality of the proposed control method.     

基于粒子群优化的混沌系统比例-积分-微分控制

基于比例-积分-微分(PID)控制算法的简单性和实用性,但对于复杂非线性系统控制时参数的难以确定问题,运用集群智能中的改进粒子群算法进行PID控制器的优化,并应用于若干混沌系统的控制.对Hénon混沌、Duffing混沌、六辊UC 轧机混沌、Nagumo-sato神经元混沌、Chen氏混沌以及永磁同步电动机混沌的控制进行了仿真研究.研究结果表明： 用PID进行混沌系统的输出反馈控制是有效的,从而拓宽了PID控制的应用范围; 用简单方法控制复杂混沌系统是完全可能的,对混沌系统的控制具有较好的参考价值; 粒子 关键词： 混沌 比例-积分-微分控制 粒子群优化算法     

Automatic control of phase synchronization in coupled complex oscillators

We present an automatic control method for phase locking of regular and chaotic nonidentical oscillations, when all subsystems interact via feedback. This method is based on the well known principle of feedback control which takes place in nature and is successfully used in engineering. In contrast to unidirectional and bidirectional coupling, the approach presented here supposes the existence of a special controller, which allows to change the parameters of the controlled systems. First we discuss general principles of automatic phase synchronization (PS) for arbitrary coupled systems with a controller whose input is given by a special quadratic form of coordinates of the individual systems and its output is a result of the application of a linear differential operator. We demonstrate the effectiveness of our approach for controlled PS on several examples: (i) two coupled regular oscillators, (ii) coupled regular and chaotic oscillators, (iii) two coupled chaotic Rössler oscillators, (iv) two coupled foodweb models, (v) coupled chaotic Rössler and Lorenz oscillators, (vi) ensembles of locally coupled regular oscillators, (vii) ensembles of locally coupled chaotic oscillators, and (viii) ensembles of globally coupled chaotic oscillators.     

A NEW SLIDING MODE CONTROL FOR A CLASS OF UNCERTAIN TIME-DELAY CHAOTIC SYSTEMS

We propose a new sliding mode control scheme for a class of uncertain time-delay chaotic systems. It is shown that a linear time invariant system with the desired system dynamics is used as a reference model for the output of a time-delay chaotic system to track. A sliding mode controller is then designed to drive the output of the time-delay chaotic system to track the desired linear system. On the sliding mode, the output of the controlled time-delay chaotic system can behave like the desired linear system. A simulation example is given in support of the proposed control scheme.     

Control of chaotic systems using an on-line trained linear neural controller

We propose a control system including an on-line trained linear neural controller to control chaotic systems. The control system stabilizes a chaotic orbit onto an unstable fixed point without using the knowledge of the location of the point and the local linearized dynamics at the point. Furthermore, the control system can track the stabilized orbit to the unstable fixed point whose location and local dynamics vary slowly with a variation of the system parameter. This paper extends a previous paper (Konishi and Kokame, 1995) for more general situations and improves the neural controller proposed in the previous paper both to simplify the training algorithm and to guarantee the convergence of the neural controller. The stability analysis of the control system reveals that some unstable fixed points cannot be stabilized in the control system. Numerical experiments show that the control system works well for controlling high-dimensional chaotic systems.     

Global Chaos Synchronization between Two New Different Chaotic Systems via Active Control

We present chaos synchronization between two new different chaotic systems by using active control. The proposed controller ensures that the states of the controlled chaotic response system asymptotically synchronizes the states of the drive system. Numerical simulations are shown to verify the result.     

一种新的分段混沌系统的同步控制

利用状态观测器思想构造驱动和响应系统，实现了一个新近提出的分段线性混沌系统的同步控制，并且推导了两个不同初值的系统实现同步的充分条件.理论分析说明该方法对原系统结构没有特殊要求，无需求解Lyapunov函数，适合应用于分段混沌系统.仿真实验的良好结果验证了该算法的有效性，对于不同初值的分段系统均能实现快速同步.同时该算法适用于一类分段混沌系统的同步控制. 关键词： 分段线性混沌系统 状态观测器 同步控制     

一种分数阶混沌系统同步的自适应滑模控制器设计

针对分数阶混沌系统的同步问题, 基于滑模控制理论和自适应控制理论, 设计了一个具有较强鲁棒性的分数阶积分滑模面, 并提出了一种自适应滑模控制器在不消除非线性项的情况下实现一类三维分数阶混沌系统同步的方法. 利用所设计的自适应滑膜控制器实现了分数阶Chen系统、分数阶Liu系统以及分数阶Arneodo系统的混沌同步. 数值模拟仿真结果验证了所设计的控制器的有效性和可行性.     

Synchronization between a novel class of fractional-order and integer-order chaotic systems via a sliding mode controller

<正>In order to figure out the dynamical behaviour of a fractional-order chaotic system and its relation to an integerorder chaotic system,in this paper we investigate the synchronization between a class of fractional-order chaotic systems and integer-order chaotic systems via sliding mode control method.Stability analysis is performed for the proposed method based on stability theorems in the fractional calculus.Moreover,three typical examples are carried out to show that the synchronization between fractional-order chaotic systems and integer-orders chaotic systems can be achieved. Our theoretical findings are supported by numerical simulation results.Finally,results from numerical computations and theoretical analysis are demonstrated to be a perfect bridge between fractional-order chaotic systems and integer-order chaotic systems.     

Hyperbolification of dynamical systems: The case of continuous-time systems

We present a new method to generate chaotic hyperbolic systems. The method is based on the knowledge of a chaotic hyperbolic system and the use of a synchronization technique. This procedure is called hyperbolification of dynamical systems. The aim of this process is to create or enhance the hyperbolicity of a dynamical system. In other words, hyperbolification of dynamical systems produces chaotic hyperbolic (structurally stable) behaviors in a system that would not otherwise be hyperbolic. The method of hyperbolification can be outlined as follows. We consider a known n-dimensional hyperbolic chaotic system as a drive system and another n-dimensional system as the response system plus a feedback control function to be determined in accordance with a specific synchronization criterion. We then consider the error system and apply a synchronization method, and find sufficient conditions for the errors to converge to zero and hence the synchronization between the two systems to be established. This means that we construct a 2n-dimensional continuous-time system that displays a robust hyperbolic chaotic attractor. An illustrative example is given to show the effectiveness of the proposed hyperbolification method.     

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.     

不确定混沌系统的反同步与参数辨识

针对一类混沌系统,提出了一种系统的混沌反同步设计方案,基于该方案,设计一种自适应控制方法,实现了参数不确定系统的混沌反同步和未知参数的辨识.数值模拟结果表明了提出方法的有效性.     

Impulsive control for Takagi--Sugeno fuzzy model with time-delay and its application to chaotic system

A control approach where the fuzzy logic methodology is combined with impulsive control is developed for controlling some time-delay chaotic systems in this paper. We first introduce impulses into each subsystem with delay of the Takagi--Sugeno (TS) fuzzy IF--THEN rules and then present a unified TS impulsive fuzzy model with delay for chaos control. Based on the new model, a simple and unified set of conditions for controlling chaotic systems is derived by the Lyapunov--Razumikhin method, and a design procedure for estimating bounds on control matrices is also given. Several numerical examples are presented to illustrate the effectiveness of this method.     

混沌系统的注入反馈控制与动态控制方法研究

提出了注入反馈控制混沌的方法,把蔡氏电路混沌系统控制到指定的平衡态和希望的振荡周期轨道上.通过改变控制参数,研究了几个典型物理状态变化现象,丰富了蔡氏电路混沌系统的应用方法 关键词： 混沌 平衡态 极限环