基于线性反馈控制的不确定混沌系统的参数辨识

基于线性反馈控制方法和Lyapunov稳定性理论,研究了参数不确定系统的混沌同步和参数辨识,设计了普遍适用的参数自适应控制律,理论证明设计的控制器可使得两个结构相同但参数不同的混沌系统渐近地达到同步,并且可以辨识出响应系统的未知参数. Lorenz系统和蔡氏电路的数值仿真进一步表明了该方法的有效性. 关键词： 不确定混沌系统 同步 参数辨识 Lyapunov函数     

不确定Chua’s电路的参数辨识与自适应同步

针对含有不确定参数的Chua’s电路,提出一种仅需传递单路信号实现混沌自适应同步的方法. 基于Lyapunov稳定性理论证明了该方法可使得两个Chua系统——驱动系统和未知参数的响应系统渐近地达到同步,并且可以辨识出响应系统的未知参数. 数值计算结果表明了该方法的有效性. 关键词： 不确定Chua’s电路 混沌同步 参数辨识 Lyapunov函数     

ADAPTIVE CONTROL AND IDENTIFICATION OF CHAOTIC SYSTEMS

A novel adaptive control and identification on-line method is proposed for a class of chaotic system with uncertain parameters. We prove that, using the presented method, a controller and identifier is developed which can remove chaos in nonlinear systems and make the system asymptotically stabilizing to an arbitrarily desired smooth orbit. And at the same time, estimates to uncertain parameters converge to their true values. The advantage of our method over the existing result is that the controller and identifier is directly constructed by analytic formula without knowing unknown bounds about uncertain parameters in advance. A computer simulation example is given to validate the proposed approach.     

Adaptive synchronization of Rossler and Chen chaotic systems

A novel adaptive synchronization method is proposed for two identical Rossler and Chen systems with uncertain parameters. Based on Lyapunov stability theory, we derive an adaptive controller without the knowledge of the system parameters, which can make the states of two identical Rossler and Chen systems globally asymptotically synchronized. Especially, when some unknown uncertain parameters are positive, we can make the controller more simple and, besides, the controller is independent of those positive uncertain parameters. All results are proved using a well-known Lyapunov stability theorem. Numerical simulations are given to validate the proposed synchronization approach.     

Chaos synchronization based on intermittent state observer

This paper describes the method of synchronizing slave to the master trajectory using an intermittent state observer by constructing a synchronizer which drives the response system globally tracing the driving system asymptotically. It has been shown from the theory of synchronization error-analysis that a satisfactory result of chaos synchronization is expected under an appropriate intermittent period and state observer. Compared with continuous control method, the proposed intermittent method can target the desired orbit more efficiently. The application of the method is demonstrated on the hyperchaotic R?ssler systems. Numerical simulations show that the length of the synchronization interval τ_s is of crucial importance for our scheme, and the method is robust with respect to parameter mismatch.     

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.     

一类含参数不确定性混沌系统的自适应控制

基于Lyaponov函数,对一类含参数不确定性混沌系统,当系统的不确定性参数具有未知界时,给出了自适应控制器的设计方法和构造控制器的解析式.构造混沌控制器直接代入控制器的参数化公式即可.方法简单,无需拼凑,能够使系统消除混沌并渐近稳定到任何期望的光滑轨道上.而整个设计过程无需预先知道未知参数的估计值和精确值.仿真验证了其有效性 关键词： 混沌系统 自适应混沌控制 Lyaponov函数 参数不确定性     

不确定混沌系统的参数识别与同步控制器的backstepping设计

设计了一种参数观测器，对不确定Rossler系统中的未知参数进行了识别，采用backstepping方法实现了异结构不确定Rossler系统和Coullet系统之间的混沌同步.根据稳定性原理，确定了同步控制器的结构和控制增益的取值范围.仿真模拟结果表明，在参数观测器和backstepping控制器的共同作用下， Coullet系统所有的状态变量严格地跟踪了不确定Rossler系统的混沌轨迹，从而证明了该观测器和控制器的有效性.     

A hybrid strategy to control uncertain nonlinear chaotic system

In this paper, a new method, based on firefly algorithm(FA) and extreme learning machine(ELM), is proposed to control chaos in nonlinear system. ELM is an efficient predicted and classified tool, and can match and fit nonlinear systems efficiently. Hence, mathematical model of uncertain nonlinear system is obtained indirectly. For higher fitting accuracy, a novel swarm intelligence algorithm FA is drawn in our proposed way. The main advantage is that our proposed method can remove the limitation that mathematical model must be known clearly and can be applied to unknown nonlinear chaotic system.     

基于观测器的模型不确定的耦合时空混沌H∞跟踪控制

考虑子系统的时空耦合作用及模型的不确定性,实现模型不确定的耦合时空混沌的 跟踪控制非常困难.然而耦合时空混沌的每个子系统用一系列模糊逻辑模型逼近,同时考虑子 系统状态的不可测性,采用模糊观测器来估计子系统的状态.由于混沌模型的很多参数和动态 特性很难准确地确定即模型具有不确定性,因此在用模糊模型逼近的同时定会产生建模误差. 基于模糊模型及状态观测器,考虑混沌模型的不确定性,提出一种Ｈ∞ 模糊跟踪控制方法,实现模型不确定性的耦合时空混沌的鲁棒跟踪控制.将控制方 案表征为求解线性矩阵不等式问题,并用凸优化方法 关键词： 耦合时空混沌 模糊模型 模糊观测器 Ｈ∞模糊跟踪控 制 线性矩阵不等式     

Robust fuzzy control for chaotic dynamics in Lorenz systems with uncertainties

This paper deals with the robust fuzzy control for chaotic systems in the presence of parametric uncertainties. An uncertain Takagi--Sugeno fuzzy model for a Lorenz chaotic system is first constructed. Then a robust fuzzy state feedback control scheme ensures the control for stable operations under bounded parametric uncertainties. For a chaotic system with known uncertainty bounds, a robust fuzzy regulator is designed by choosing the control parameters satisfying the linear matrix inequality. To verify the validity and effectiveness of the proposed controller design method, an analysis technique is suggested and applied to the control of an uncertain Lorenz chaotic system.     

Parameter identification and synchronization of spatiotemporal chaos in an uncertain Gray-Scott system

The zero-asymptotic property of sliding variables in discrete systems is extended to a continuous one and applied to partial differential equations which describe spatiotemporal chaos. A method of chaos synchronization and parameter identification is proposed. The synchronization controllers and the parameter recognizers are designed. The uncertain Gray-Scott system is taken as an example to verify the effectiveness of the method. Simulation results show that the identification variables in the parameter recognizers may take the place of the unknown parameters in both target and response systems. Global synchronization of the two spatiotemporal chaotic systems with uncertain parameters may be realized quickly after controllers are added. Supported by the Natural Science Foundation of Liaoning Province, China (Grant No. 20052151) and the Innovative Team Program of Liaoning Educational Committee     

多项式混沌展开的浅海水声环境参数敏感度分析*

水下声场是海洋环境参数的非线性函数,因此环境参数的不确定性必然会引起水下声场预测的不确定性,从而导致与声场预测相关的声呐探测和水声通信等设备性能的下降。该文将Sobol敏感度指数的计算与多项式混沌展开方法相结合,将敏感度指数表达为环境条件的函数,利用Q范数约束的双曲截断方案来减少多项式项数,有效地分析了设定的"浅海负梯度温跃层"信道中8个环境参数及其交互效应对水下声传播的影响。结果表明,沉积层声速是低频远距离声场不确定性分布的最主要贡献参数,同时对于下发下收的情况,声源深度的影响程度随着声源频率增加而逐渐增大。最后应用射线理论从海底反射的角度解释了各个环境因素影响程度差异的具体原因。该文的研究对水声通信和探测系统在浅海不确定环境下的性能预报研究具有重要的参考意义。     

异结构不确定混沌系统的同步控制与参数识别

设计了一种同步控制器和参数识别器来实现异结构不确定混沌系统的同步控制。以单模激光Lorenz系统和不确定Genesio系统为例,验证了这种控制器的有效性。根据Lyapunov稳定性理论,分步构造出Lyapunov函数,从而给出同步控制器和参数识别器的结构。仿真结果表明：利用本文提出的同步控制方案,仅用一个控制器就能使不确定Genesio系统的所有状态变量严格地跟踪Lorenz系统的混沌轨迹,而且误差变量经过短暂的时间序列以后始终平稳地趋于零,实现了异结构混沌系统的混沌同步,且不确定Genesio系统的参数全部可以得到识别。     

外加正弦驱动力抑制一类分段光滑系统的混沌运动

针对含间隙碰撞振动的机械系统由于参数的改变，产生分叉和混沌运动，造成原稳定运行的系统产生异常振动时的故障消除方法展开研究.用外加正弦驱动力抑制混沌运动.提出了一种外加驱动力参数调节算法.该算法以原系统稳定运行时的可测状态量为希望目标，根据实际输出与希望目标的误差值，实时产生并逐步微调节至所需外加驱动力.通过对一个典型含间隙往复碰撞模型的数值仿真，检验了该方法的有效性. 关键词： 混沌抑制 碰撞振动 间隙 机械系统     

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.     

不确定自催化反应扩散时空混沌系统的延时同步

设计了一种延迟同步控制器实现了时空混沌系统之间的同步控制.基于Lyapunov稳定性定理,确定了延迟同步控制器的结构以及系统状态变量之间的误差方程.以自催化反应扩散时空混沌系统为例,仿真模拟验证了该控制器的有效性.进一步设计了参量辨识器,对不确定自催化反应扩散时空混沌系统中的参量进行了有效辨识.通过研究有界噪声影响下系统的同步效果,表明该同步方法具有较好的抗干扰能力. 关键词： 时空混沌 延时同步 参量辨识 有界噪声     

复Ginzburg-Landau方程时空混沌的网络同步与参量辨识

研究了参量未知的时空混沌系统构成复杂网络的同步与参量辨识问题. 设计的参量辨识律可以有效地辨识复杂网络中所有节点时空混沌系统中的未知参量. 基于稳定性定理, 通过构造适当的Lyapunov函数, 确定了网络完全同步的条件. 以参量未知的一维复Ginzburg-Landau方程作为网络节点为例, 通过仿真模拟检验了参量辨识律以及同步方法的有效性.     

陈氏混沌系统的自适应控制

通过简单的线性状态反馈方法,分别在系统参数已知和未知的情况下研究了陈氏混沌系统的控制问题.当参数已知时,给出了反馈增益的范围;当参数未知时,设计了一自适应控制器,它克服了一般的自适应控制器中控制律不连续的缺点.通过实验仿真证明了所给方法的有效性. 关键词： 陈氏混沌系统 混沌控制 自适应控制     

一类不确定混沌系统的观测器同步

基于降维观测器的方法实现了一类具有外部扰动的混沌系统的同步. 无需知道系统外部扰动项的任何信息，就可对驱动系统设计基于降维观测器的响应系统，从而实现了混沌系统的同步. 数值仿真表明该方法是有效的. 关键词： 混沌同步 混沌系统 观测器