Synchronization and Parameters Identification of Chaotic Systems via Adaptive Control

Based on Lyapunov stability theory, a novel adaptive controller is designed for a class of chaotic systems. The parameters identification and synchronization of chaotic systems can be carried out simultaneously. The controller and the updating law of parameters identification are directly constructed by analytic formula. Simulation results with Chen‘s system and Roessler system show the effectiveness of the proposed controller.     

Synchronization of Chaotic Systems Using Time-Delayed Fuzzy State-Feedback Controller

This paper presents the fuzzy-model-based control approach to synchronize two chaotic systems subject to parameter uncertainties. A fuzzy state-feedback controller using the system state of response chaotic system and the time-delayed system state of drive chaotic system is employed to realize the synchronization. The time delay which complicates the system dynamics makes the analysis difficult. To investigate the system stability and facilitate the design of fuzzy controller, Takagi-Sugeno (T-S) fuzzy models are employed to represent the system dynamics of the chaotic systems. Furthermore, the membership grades of the T-S fuzzy models become uncertain due to the existence of parameter uncertainties which further complicates the system analysis. To ease the stability analysis and produce less conservative analysis result, the membership functions of both T-S fuzzy models and fuzzy controller are considered. Stability conditions are derived using Lyapunov-based approach to aid the design of fuzzy state-feedback controller to synchronize the chaotic systems. Simulation examples are presented to illustrate the merits of the proposed approach.     

基于投影法的不确定分数阶混沌系统自适应同步

针对一类具有未知参数、未知非线性函数及外部扰动的分数阶混沌系统,基于分数阶系统稳定性理论和Lyapunov稳定性理论,该文提出一种基于滑模自适应和投影法的同步控制策略。首先选取一类稳定的分数阶积分滑模面,运用自适应技术对不确定项进行估计,设计了同步控制器。然后对自适应设计中容易出现的增长型自适应律运用投影法进行修正,以保证参数有界,从而也保证控制输入有界。最后数值仿真证明了所设计控制器的正确性和有效性。     

离散动力系统无退化-配置N个正Lyapunov指数

针对离散时间混沌动力学系统,该文提出一种基于矩阵特征值以及特征向量配置Lyapunov指数为正的新算法。计算离散受控矩阵的特征值以及特征向量,设计一类具有正Lyapunov指数的通用控制器,理论证明系统轨道的有界性和Lyapunov指数的有限性。对线性反馈算子以及微扰反馈算子进行数值仿真分析,验证了算法的正确性、通用性和有效性。性能评估表明,与Chen-Lai算法相比,该方法可以构建较低计算复杂度的混沌系统,并且运行时间较短,其输出序列也具有较强的随机性,实现了无退化、无兼并的离散混沌系统。     

Globally Exponential Synchronization and Parameter Regulation for Coupled Chaotic System via Adaptive Control

Based on Lyapunov stability theory,an adaptive controller is designed for a class of chaotic systems. Globally exponential synchronization and parameter regulation for couple chaotic systems can be carried out simultaneously. The controller and the regulating law of parameters are directly constructed by analytic formula. Simulation results with some chaotic systems show the effectiveness of the proposed controller.     

Chaos Synchronization on Parameters Adaptive Control for Chen Chaotic System

1　IntroductionThesynchronizationoftwononlineardynamicalsystemsisaphenomenonofimportanceinawiderangofappliedsciences,andhasbeenpaidmuchat tentiontoandinvestigatedinthe pasttwentyyears[1～ 1 3] .Recentlysecurecommunicationusingchaossynchronizationhasbeenpaidmuchattentiontoasoneoftheimportantpracticalapplicationsofchaos[1 4 ] .Themainideaisthatwhenaninforma tionsignalismaskedbythechaoticsignal,itcanbeeasilyrecoveredatthereceiverbymeansofchaossynchronization ,whileexternalattackisalmostim possibl…     

用李雅谱诺夫指数配置法控制统一混沌系统

解析设计控制器，通过配置相应的李雅谱诺夫指数，使统一混沌系统趋于预期点．由于受控后系统李雅谱诺夫指数具有先知性，因此，我们可以根据需要改变李雅谱诺夫指数的大小来控制系统收敛速度．设计还表明，受控的统一混沌系统的收敛情况与参数无关。     

Fuzzy neural networks for direct adaptive control

It is well known that sliding-mode control is simple and insensitive to uncertainties and disturbances. However, control input chattering is the main problem of the classical sliding-mode controller (SMC). In this paper, a fuzzy neural network SMC (FNNSMC) is presented for a class of nonlinear systems. The FNNSMC can eliminate the chattering, unlike the SMC, but there is larger rising time in the FNNSMC than in the SMC. In some cases, small rise time is important. To decrease the rising time of the FNNSMC, an adaptive controller is proposed where the SMC and the FNNSMC are incorporated by a smooth transformation. This adaptive control scheme can improve the dynamical performance and eliminate the high-frequency chattering in the control signal. The system stability is proved by using the Lyapunov function. The simulation results demonstrate the advantages of the proposed adaptive controller.     

Dynamics modeling and deviation control of the composites winding system

During the composites winding process, running speed, tension fluctuation and other factors often lead to the tape deviation. To improve the winding precision and eliminate the running deviation, lateral dynamics of the tape winding is analyzed and mathematical model of the rectifying system is established. Then, a novel adaptive sliding mode controller (ASMC) is proposed, and principle of this control scheme is employing two fuzzy systems to approximate the nonlinear functions and utilizing another two fuzzy systems to adjust the feedback gain (FG) and switching gain (SG). Stability and convergence of the control system can be guaranteed by the Lyapunov theory and Barbalat Lemma. Simulation and experimental results show that the designed ASMC has highest control precision and much smaller input chattering when compared with other controllers.     

条件Lyapunov指数和时间τ-条件Lyapunov指数的研究

本文研究条件Ｌｙａｐｕｎｏｖ指数与τ指数的定义、求解技术及其应用。两种指数从不同角度对系统本质特性进行刻划,条件Ｌｙａｐｕｎｏｖ指数在混沌同步中有重要应用,近来它还衩用来进行相空间重构问题的研究。时间τ－条件Ｌｙａｐｕｎｏｖ指数是一类利用状态变量的离散采样作驱动信号的脉冲方式的重要定量指标。本文提出一种简便的求解技术,在Ｗｏｌｆ求解Ｌｙａｐｕｎｏｖ指数谱程序的基础上,稍加改动即可使其适用于Ｌｙａｐ     

Adaptive Control of Two-Axis Motion Control System Using Interval Type-2 Fuzzy Neural Network

An interval type-2 fuzzy neural network (IT2FNN) control system is proposed for the precision control of a two-axis motion control system in this paper. The adopted two-axis motion control system is composed of two permanent-magnet linear synchronous motors. In the proposed IT2FNN control system, an IT2FNN, which combines the merits of an interval type-2 fuzzy logic system and a neural network, is developed to approximate an unknown dynamic function. Moreover, adaptive learning algorithms that can train the parameters of the IT2FNN online are derived using the Lyapunov stability theorem. Furthermore, a robust compensator is proposed to confront the uncertainties, including a minimum reconstructed error, optimal parameter vectors, and higher order terms in Taylor series. To relax the requirement for the value of the lumped uncertainty in the robust controller, an adaptive lumped uncertainty estimation law is also investigated. Last, the proposed control algorithms are implemented in a TMS320C32 digital-signal-processor-based control computer. From the simulated and experimental results, the contour tracking performance of the two-axis motion control system is significantly improved, and the robustness can be obtained as well using the proposed IT2FNN control system.     

一类混沌电路的跃变参数识别与同步*

基于李亚普诺夫稳定性理论和矩阵理论,用两种方法对一类混沌电路系统参数发生跃变情况下的参数识别与同步控制进行了理论分析和数值计算机模拟。第一种方法是通过负反馈将系统镇定到某个稳定态来识别系统的跃变参数（系统参数突然发生阶跃性变化）,通过计算李亚普诺夫指数获得反馈系数临界值。第二种方法是基于李亚普诺夫稳定性理论得到的参数观测器包含了可调节的增益系数,当两个混沌系统达到完全同步时驱动系统的5个未知参数在阶跃变化情况下也可以被准确识别。最后对两种方法的优缺点进行了比较和分析。     

A Robust Hybrid Intelligent Position/Force Control Scheme for Cooperative Manipulators

We examine in this paper the complex problem of simultaneous position and internal force control in multiple cooperative manipulator systems. This is done in the presence of unwanted parametric and modeling uncertainties as well as external disturbances. A decentralized adaptive hybrid intelligent control scheme is proposed here. The controller makes use of a multi-input multi-output fuzzy logic engine and a systematic online adaptation mechanism. Unlike conventional adaptive controllers, the proposed controller does not require a precise dynamical model of the system's dynamics. As a matter of fact, the controller can achieve its control objectives starting from partial or no a priori knowledge of the system's dynamics. The ability to incorporate the already acquired knowledge about the system's dynamics is among what distinguishes the proposed controller from its predecessor adaptive fuzzy controllers. Using a Lyapunov stability approach, the controller is proven to be robust in the face of varying intensity levels of the aforementioned uncertainties. The position and the internal force errors are also shown to asymptotically converge to zero under such conditions     

Generating Multi-Scroll Chaotic Attractors via?Switched Fractional Systems

A method is presented to generate multi-scroll chaotic attractors by switched fractional systems. Two sub-models in this structure are constructed by different piecewise-linear functions. It is proved that the switched systems can demonstrate multi-scroll chaotic attractors with suitable parameters and switching rule. Moreover, in order to obtain the multi-scroll chaotic attractors with the lowest system order, the relationship between Lyapunov exponents and parameters is studied. It is found that the multi-scroll chaotic attractors can be presented with a system order larger than 0.9. Numerical examples are provided to illustrate the effectiveness of the proposed scheme.     

空天飞行器模糊自适应轨迹线性化控制器设计

针对一类单输入单输出非线性不确定系统,提出了模糊自适应轨迹线性化控制(TLC)方法并应用于空天飞行器(ASV)飞行控制系统设计.利用模糊系统具有以任意精度逼近非线性系统的能力对未知干扰和不确定进行估计,以减小其对系统性能的影响,并通过鲁棒控制项来克服模糊系统的逼近误差.采用Lyapunov方法,证明了闭环系统所有信号一致最终有界.最后利用提出的控制方案设计了空天飞行器飞行控制系统,并在高超声速条件下进行了仿真验证,仿真结果表明了该方法的有效性和鲁棒性.     

一种四螺旋混沌系统仿真研究

为了改善Lü系统的混沌特性,通过在混沌Lü系统上添加一维线性状态反馈控制器,构建了一个新的四维连续自治混沌系统,得到了奇异的四螺旋鲁棒混沌吸引子。利用相轨图、Lyapunov指数谱等数值方法,其最大Lyapunov指数为正值且几乎恒定不变,系统具有很好的鲁棒性.随控制参数变化,系统能够从四螺旋混沌吸引子演变成双螺旋混沌吸引子。通过在混沌Lü系统电路上外加一个简单的线性积分电路实现了新混沌系统的实验电路,实验仿真与数值方法所得结果有着很好的一致性。     

基于模糊感觉强度的无规则模糊逻辑系统的仿真设计

基于模糊逻辑方法在心理语言学研究领域的有效性,该文提出基于模糊感知强度和韦伯定律的一类新的无规则模糊逻辑系统及其自适应控制应用的方法。首先,应用心理物理学中的概念,模糊逻辑系统的知识库是利用模糊感觉强度来描述专家经验感受;模糊推理后应用广义韦伯定律进行解模糊得到系统输出。然后,针对一类非线性系统,利用构造的新的无规则模糊逻辑系统进行自适应控制设计,得到相应的控制器和参数自适应律。最后,通过Duffing混沌系统仿真算例验证了该文方法的可行性和有效性。     

Nonlinear adaptive control of direct-drive brushless DC motors andapplications to robotic manipulators

Robust adaptive nonlinear control of brushless DC (BLDC) motors is considered. A controller is designed for the plant that is robust to parametric and dynamic uncertainties in the entire electromechanical system. These uncertainties are shown to be bounded by polynomials in the states. In addition, the controller can reject any bounded unmeasurable disturbances entering the system. A model for the motor incorporating magnetic saturation is used to design voltage-level control inputs for the motor. The design methodology is based on our earlier work on adaptive control of nonlinear systems. The overall stability of the system is shown using Lyapunov techniques. The tracking error is shown to be globally uniformly bounded. The design procedure is shown to be also applicable to multilink manipulators actuated by BLDC motors. The performance of the controller is verified through simulations and comparisons with a proportional-integral-derivative-type controller are made     

A no-equilibrium memristive system with four-wing hyperchaotic attractor

A new memristive system is proposed in this paper which can have no equilibrium and a line of equilibrium based on the value of its controlling parameter. Also, changing that parameter can cause the system having both chaotic and hyperchaotic solutions. This system has a multi-wing strange attractor. Dynamical properties of this system such as Lyapunov exponents and bifurcation diagram are calculated. This system belongs to the category of systems with hidden and multistable attractors. A system with all the above-mentioned properties is not common in the literature. Finally, an adaptive sliding mode control method is applied to synchronize this chaotic system.