基于参数自适应方法的统一混沌系统的同步控制

采用参数自适应控制方法，根据Lyapunov稳定性原理，通过构造适当的控制函数和设计参数的自适应控制律，分别实现了系统在不同确定参数和相同不确定参数两种情况下的统一混沌系统的同步导出在这两种情况下的统一混沌系统能实现同步的充分条件.相同不确定参数情况下的同步系统控制器结构更简单、同步性能更优．数值仿真证明了该方法的有效性．     

一类参数不确定混沌系统的广义同步

针对一类混沌系统,研究了参数未知的混沌系统的广义同步．基于lyapunov稳定性定理和自适应控制方法,给出了自适应控制器和参数自适应律的解析表达式．将该方法应用于参数未知的新混沌系统,理论证明了该方法可以使新混沌系统达到渐近的广义同步,并且可以辨识出系统的未知参数．数值模拟进一步证明了该方法的有效性．     

连续时间混沌系统的参数自适应控制1)

研究了连续时间混沌系统的参数自适应控制,提出了关于多重参数混沌非线性系统的参数自适应控制的新方法.考虑系统参数是线性形式的自适应控制,利用Lyapunov方法证明了参数控制方程是全局渐近稳定的.研究结果表明该控制方法是分析混沌参数自适应控制的一个十分有效的方法.     

不确定参数时滞混沌系统的自适应反同步

研究超混沌系统的反同步问题,针对一类异结构参数不确定存在时滞超混沌系统的反同步问题,提出了一种设计控制律的新方法.以李雅普诺夫稳定性理论为基础,通过自适应控制法设计了非线性控制器和参数自适应律,实现含不确定参数的时滞混沌系统的反同步控制,并运用拉萨尔不变集理论建立的李亚普诺夫稳定性原理证明了误差系统是渐近稳定的.最后,利用MATLAB对超混沌Lu系统与超混沌Chen系统的数值仿真,验证了所提出方法的有效性和正确性.     

一类受迫振荡混沌系统的自适应控制

针对一类受迫振荡混沌系统,提出了一种普遍适用的自适应控制方法,给出了自适应控制器及参数自适应律的设计方法.基于Lyapunov稳定性理论,证明了系统的稳定性.仿真实验表明,本文所提方法避免了混沌系统中除受迫振荡项外的不确定参数的影响,实现了一类混沌系统的有效控制及受迫振荡项参数的准确辨识,方法具有良好的可实现性和工程应用价值.     

不确定混沌系统的自适应滑模变结构同步

针对一类不确定混沌系统,运用自适应滑模变结构控制方法,设计了相应的控制器和自适应律,实现了混沌系统的主从同步控制.通过构造Lyapunov函数在理论上证明了该同步方法的有效性,并且在不确定项上界未知的情况下,对系统未建模部分和噪声干扰具有很强的鲁棒性.最后以Duffing-Holmes系统为例,进行了混沌同步仿真,仿真结果表明该方法的有效性.     

参数不确定离散混沌系统的模糊脉冲控制

研究了参数不确定离散混沌系统的控制问题.通过Takagi-Sugeno(TS)模糊动态模型和脉冲控制技术,建立了参数不确定离散混沌系统的Takagi-Sugeno模糊脉冲控制模型,然后利用矩阵分析和Lyapunov稳定性理论,得到了参数不确定离散混沌系统控制的一个充分条件,最后通过实例证实了该结果的正确性,相比传统的控制方法,基于Takagi-Sugeno模型的模糊脉冲控制方法具有一定的优越性.     

连续时间混沌系统的参数自适应控制

研究了连续时间混沌系统的参数自适应控制,提出了关于多重参数混沌非线性系统 的参数自适应控制的新方法.考虑系统参数是线性形式的自适应控制,利用Lyapunov方法 证明了参数控制方程是全局渐近稳定的.研究结果表明该控制方法是分析混沌参数白适应控 制的一个十分有效的方法.     

基于非线性观测器设计的混沌同步控制

提出一种基于非线性观测器设计的混沌同步控制方法,给出了一类含有不确定参数混沌系统的观测器实现条件.该控制策略可满足混沌系统中存在一些不确定参数的要求.通过对Lorenz混沌系统的理论分析和数字仿真,证明了其有效性.     

一个新混沌系统的参数不确定自适应同步

针对一个新的混沌系统,简单分析了其稳定性,并对其进行同步控制.在研究单变量驱动同步的基础上,应用自适应控制理论,研究了当系统参数不确定时的同步问题.根据Lyapunov稳定性理论,推导了当参数不确定时误差系统渐近稳定的充分条件,构造了合适的自适应控制规律快速辨识了系统参数.数值仿真结果表明方法是有效的和可行的,且自适应控制规律的设计简单可靠,并实现了两个混沌系统的状态同步.同时该方法可推广到情况类似的其他混沌系统.     

Synchronizing chaotic systems with parametric uncertainty via a novel adaptive impulsive observer

This paper proposes a new class of observers, called adaptive impulsive observers. These observers are capable of estimating the states and unknown parameters of an uncertain system using the output of the system at discrete jump times only. Through a proposed theorem, the stability of the states estimation error system is proved and an upper bound on the maximum possible impulses (jumps) interval is given. Due to these advantages, the proposed adaptive impulsive observer is used in a chaotic systems synchronization scheme. The presented simulation results show the effectiveness of the proposed observer even when the coupling signal is scalar. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

参数不确定的广义Lorenz系统的同步研究

针对参数不确定的广义Lorenz混沌系统,提出一种新的自适应反馈同步方法。利用Lyapunov稳定性理论,设计了参数不确定的广义Lorenz混沌系统的自适应反馈同步控制器,并给出了参数自适应律的解析式。理论上证明了所设计控制器的正确性,并通过Matlab进行仿真实验,成功地实现了系统状态同步和系统不确定参数的辨识。数值仿真结果验证了所提出方法的可行性和有效性。该方法同步建立时间短,同步精度高,对系统初值没有特殊要求。     

Adaptive synchronization on uncertain dynamics of high-order nonlinear multi-agent systems with partition of unity approach

An adaptive synchronization of uncertain chaotic system is presented using partition of unity method. First, the uncertainties of chaotic systems are approximate by the linear combination of partition of unity. Subsequently, the sliding mode adaptive controllers are proposed for synchronization of the uncertain chaotic systems. The proposed approach offers a systematic design procedure for adaptive synchronization of a class of uncertain chaotic system in the chaos research literature. We also illustrate examples of chaotic systems such as Chen and Lorenz chaotic systems to show the effectiveness of the approach.     

Adaptive‐impulsive consensus of multiagent systems

This paper studies the leader‐following consensus problem of multiagent nonlinear systems with uncertain parameters and control gain error. On the basis of the theory of impulsive differential equations, the adaptive control technique, and the Lyapunov stability theory, some novel adaptive‐impulsive consensus conditions are given to realize the consensus of a class of multiagent nonlinear systems. Compared with the existing investigations on the impulsive consensus of multiagent systems, the proposed impulsive control protocol with uncertain parameters and control gain error is more rigorous and effective in practical systems. Four numerical simulations are verified to confirm the effectiveness of the proposed methods.     

不确定参数下离散混沌系统的开闭环控制

在很多实际环境中，系统模型参数经常是不确定的，使离散混沌系统的控制策略可能不再有效。当参数不能直接观测时，开闭环控制方案将由于不精确的系统模型而失效。针对这个问题，提出了参数自适应开闲环控制策略来控制不确定参数的离散混沌系统。对开闲环控制在不确定参数条件下，参数变化满足控制需要的条件进行了讨论。同时，提出了参数自适应开闲环控制，将原有的开闭环控制推广到更大的范围。从Henon系统的仿真中，参数自适应开闲环控制策略显示了良好的抗扰动特性。     

参数不确定混沌系统的时滞同步

当混沌系统参数不确定时,采用自适应控制方法,研究了系统间的时滞同步问题。基于Lyapunov稳定性理论,给出了同步条件,并识别出了系统的未知参数。理论推导严格证明了结果的正确性;同时,以Lorenz系统为例进行了数值仿真与说明。     

Neural network-based synchronization of uncertain chaotic systems with unknown states

In this paper, synchronization of chaotic systems with unknown parameters and unmeasured states is investigated. Two nonidentical chaotic systems in the framework of a master and a slave are considered for synchronization. It is assumed that both systems have uncertain dynamics, and states of the slave system are not measured. To tackle this challenging synchronization problem, a novel neural network-based adaptive observer and an adaptive controller have been designed. Moreover, a neural network is utilized to approximate the unknown dynamics of the slave system. The proposed method imposes neither restrictive assumption nor constraint on the dynamics of the systems. Furthermore, the stability of the entire closed-loop system in the presence of the observer dynamics has been established. Finally, effectiveness of the proposed scheme is demonstrated via computer simulation.     

Adaptive Synchronization of Uncertain Chaotic Systems Based on T–S Fuzzy Model

This paper presents an adaptive approach for synchronization of Takagi-Sugeno (T-S) fuzzy chaotic systems. T-S fuzzy model can represent a general class of nonlinear system and we employ it for fuzzy modeling of the chaotic drive system. Since the output of the drive system is only available for synchronization, the response system is designed based on fuzzy adaptive observer for uncertain parameters and parameter mismatch cases. We analyze the stability of the overall fuzzy synchronization system by applying Lyapunov stability theory and derive stability conditions by solving linear matrix inequalities (LMIs) problem. The adaptive law is derived to estimate the uncertain parameters or parameter mismatch. Numerical examples are given to demonstrate the validity of the proposed fuzzy adaptive synchronization approach.     

Hybrid function projective synchronization of chaotic systems with uncertain time-varying parameters via Fourier series expansion

In this paper, the hybrid function projective synchronization (HFPS) of different chaotic systems with uncertain periodically time-varying parameters is carried out by Fourier series expansion and adaptive bounding technique. Fourier series expansion is used to deal with uncertain periodically time-varying parameters. Adaptive bounding technique is used to compensate the bound of truncation errors. Using the Lyapunov stability theory, an adaptive control law and six parameter updating laws are constructed to make the states of two different chaotic systems asymptotically synchronized. The control strategy does not need to know the parameters thoroughly if the time-varying parameters are periodical functions. Finally, in order to verify the effectiveness of the proposed scheme, the HFPS between Lorenz system and Chen system is completed successfully by using this scheme.