Adaptive Fuzzy Control of Nonlinear in Parameters Uncertain Chaotic Systems Using Improved Speed Gradient Method

This paper presents an adaptive fuzzy controller for Nonlinear in Parameters (NLP) chaotic systems with parametric uncertainties. In the proposed controller, the unknown parameters are estimated by the novel Improved Speed Gradient (ISG) method, which is a modification of Speed Gradient (SG) algorithm. ISG employs the Lagrangian of two suitable objective functionals for on-line estimation of system parameters. The most significant advantage of ISG is that it is applicable to NLP systems and it results in a faster rate of convergence for the estimated parameters than the SG method. Estimated parameters are used to design the fuzzy controller and to calculate the Lyapunov exponents of the chaotic system adaptively. Furthermore, established on the well-known Takagi–Sugeno (T-S) fuzzy model, a LMI (Linear Matrix Inequality)-based fuzzy controller is designed and is tuned using estimated parameters and Lyapunov exponents. Throughout the controller design procedure, several important issues in fuzzy control theory including relaxed stability analysis, control input performance specifications, and optimality are taken into account. Combination of ISG parameter estimation method and T-S-based fuzzy controller yields an adaptive fuzzy controller capable to suppress uncertainties in parameters and initial states of NLP chaotic systems. Finally, simulation results are provided to show the effectiveness of the ISG and adaptive fuzzy controller on chaotic Lorenz system and Duffing oscillator.     

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.     

Chen系统和一类统一混沌系统的同步控制

本文利用Lyapunov方法讨论了Chen系统的同步问题以及一类包含Chen系统与Lorenz系统的统一混沌系统的同步问题，所构造的状态反馈同步控制器仅需要一个状态变量，并进行了数值模拟。     

混沌动力学系统的神经网络学习控制研究

针对混沌动力学系统建模困难，控制不易实现，存在干扰等特点，在附加动量法的自适应BP网络的基础上，研究了混沌动力学系统的学习控制策略。构建了混沌动力学系统的NN模型和NN控制器，对混沌系统在学习的同时施加控制，仿真实验结果表明，该控制策略具有鲁棒性强，有良好的适应性，网络参数训练时间短等优点。     

Adaptive synchronization of Chen chaotic system with uncertain parameters

By the control method independent of system parameters, synchronization of two Chen chaotic systems with identical, but uncertain parameters is discussed in this article. Based on Lyapunov’s theorem, an adaptive controller and the parameters estimate update law are derived to make the solution of the error dynamical equation converge at the point E(0, 0, 0) with a quick speed, that is, the states of two Chen chaotic systems can be asymptotically synchronized. Numerical simulations verify the effectiveness and the adaptivity to the variation of Chen system parameters.     

连续混沌系统的自适应同步控制方法

针对混沌同步过程中参数摄动而带来的同步困难问题,提出一种自适应同步控制规则,并根据此控制规则设计自适应控制器,理论分析和仿真实验表明该规则可完成对不确定参数和不同初始条件下的连续混沌系统的参数辨识和同步控制。     

基于线性状态反馈方法的Nadolschi混沌系统同步

研究了一类新型混沌系统——Nadolschi系统的同步控制问题。首先为响应系统设计一个多变量线性状态反馈控制器,进而将Nadolschi系统的同步控制问题转化为误差系统零平衡点的镇定问题。然后,根据Lyapunov稳定性理论,得出使Nadolschi混沌系统达到渐近同步的充分条件。仿真结果验证了所提方法的有效性,所设计的控制器具用结构简单,易于实现等优点。     

A Control Lyapunov Function Approach to Stabilization of Affine Nonlinear Systems with Bounded Uncertain Parameters

This paper considers the robust stabilization problem of a class of affine nonlinear systems with bounded uncertain time-invariant parameters. A robust control Lyapunov function (RCLF) is introduced for the considered system. Based on the RCLF, a globally asymptotically stabilizing controller is then designed. The proposed controller is robust under the variant of system parameters. As the applications of the proposed scheme, the stabilization of uncertain feedback linearizable systems and the unified chaotic system are investigated, respectively. A numerical example on the unified chaotic system is also provided to illustrate the effectiveness of the presented method.     

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.     

State-Space Self-Tuning Control for Stochastic Fractional-Order Chaotic Systems

Based on the modified state-space self-tuning control (STC), a novel low-order tuner via the modified observer/Kalman filter identification (OKID) is proposed for stochastic fractional-order chaotic systems. The OKID method is a time-domain technique that identifies a discrete input-output map by using known input-output sampled data in the general coordinate form, through an extension of the eigensystem realization algorithm (ERA). First, the estimated system in the general coordinate based on the conventional OKID method is transformed to the one in an observer form to fit the state-space innovation form for the STC. Then, in stead of the conventional recursive least squares (RLS) identification algorithm used for STC, the Kalman filter as a parameter estimator with the state-space innovation form is presented for effectively estimating the time-varying parameters. Besides, taking the advantage of the digital redesign approach, the derivation of the current-output-based observer is proposed for the modified STC. As a result, the low-order state-space self-tuner with the high-gain controller property is then proposed for stochastic fractional-order chaotic systems, which the fractional operators are well approximated using the standard high integer-order operators. Finally, the fractional-order Chen and Roumlssler systems with stochastic system process and measurement noises are used as illustrative examples to demonstrate the effectiveness of the proposed methodology     

A Pulsed Control Method for Chaotic Systems

In this paper, it is proposed a method for controlling chaotic systems; where the main goal is to obtain a periodic behaviour for a chaotic system. In our approach, the system to control is considered as a black-box, and therefore it is not necessary to know a mathematical model of the system, only experimental measurements are used. Our method employs pulses with adjustable amplitude and width, and it is implemented in discrete time. In order to generate pulses control, a variable Poincaré section is used; which is computed on-line using a moving average sampling signal. Measurement noise is considered too, by means of an additional controller parameter (hold-off time), resulting that controller tuning is made using four parameters: proportional gain, sampling time, pulse width and hold-off time. In order to test the proposed method, computer simulations with several representative chaotic systems (Lorenz, Chua, Chen, Colpitts and others) are carried out and satisfactory results are obtained.     

Identification and control of continuous-time nonlinear systems via dynamic neural networks

In this paper, we present an algorithm for the online identification and adaptive control of a class of continuous-time nonlinear systems via dynamic neural networks. The plant considered is an unknown multi-input/multi-output continuous-time higher order nonlinear system. The control scheme includes two parts: a dynamic neural network is employed to perform system identification and a controller based on the proposed dynamic neural network is developed to track a reference trajectory. Stability analysis for the identification and the tracking errors is performed by means of Lyapunov stability criterion. Finally, we illustrate the effectiveness of these methods by computer simulations of the Duffing chaotic system and one-link rigid robot manipulator. The simulation results demonstrate that the model-based dynamic neural network control scheme is appropriate for control of unknown continuous-time nonlinear systems with output disturbance noise.     

一种可完全线性化的不同类型混沌系统同步方法

讨论可完全线性化的不同类型混沌系统之间的同步问题.根据滑模控制原理求取混沌同步控制形式,利用扩张状态观测器对系统信息进行渐进估计,把复杂的滑模控制策略变为可实现的控制方式,以此实现具有不确定性混沌系统的同步.以Duffing和Vander Pol系统为例进行仿真,效果良好.     

Chaotic Synchronization Using Sampled-Data Fuzzy Controller Based on Fuzzy-Model-Based Approach

This paper presents the synchronization of chaotic system using a sampled-data fuzzy controller. To carry out the system analysis, a fuzzy model is employed to represent the chaotic systems. Linear-matrix-inequality (LMI)-based system stability and performance conditions are derived using a Lyapunov-based approach. The derived LMI-based stability and performance conditions are employed to aid the design of a stable and well-performing sampled-data fuzzy controller to achieve the synchronization of chaotic systems. An application example is given to illustrate the merits of the proposed approach.     

一类非线性系统的混沌反控制研究

针对一类非线性系统的混沌反控制问题,借用非线性状态观测器概念设计实现混沌反控制的控制器。非混沌系统在控制器的控制下,在与混沌系统的输出实现同步的同时,使非混沌系统处于混沌状态,实现混沌反控制的目标。理论分析及仿真结果都证明该方案的有效性和可行性。     

一类混沌系统的动态输出反馈控制

为了对一类混沌系统实施控制,提出了利碍新的控制器来控制混沌系统。以往的混沌控制方法只针对个别特殊的混沌系统,而利用动态输出反馈的方法能控制一类混沌系统,这方面的工作以前也曾有过。利用李雅普诺夫稳定理论,结合线性矩阵不等式优化方法,分析了系统的稳定性。数值仿真也表明了所提出的控制策略的有效性。     

不确定蔡氏电路混沌系统的神经网络优化控制

该文研究了不确定非线性蔡氏电路混沌系统的动态神经网络在线辨识和跟踪控制问题.利用无源技术得出梯度下降算法调整神经网络辨识器权值的稳定性定理,然后在辨识模型基础上设计局部优化控制器,将蔡氏混沌系统镇定到期望目标轨迹,并保证跟踪误差有界.数值仿真结果表明了所提出方法的有效性.     

Taming Single Input Chaotic Systems by Fractional Differentiator-Based Controller: Theoretical and Experimental Study

A simple fractional differentiator-based controller is proposed to suppress chaos in a 3D single input chaotic system by stabilizing some of the fixed points. The tuning procedure for the proposed controller is based on the stability concepts in the incommensurate fractional order systems. To show the efficiency of the controller, some numerical simulations are given. Also, to evaluate the practical capability of the proposed controller, we experimentally apply it to control chaos in a chaotic circuit. Moreover, some mathematical analyses are presented to show the applicability of the proposed controller, when its structure is not exactly implementable.     

混沌系统的动态神经网络自适应控制

针对混沌系统模型误差,该文提出一种非线性鲁棒自适应辨识和控制新方法,目标是通过下面两个步骤将混沌系统镇定到不动点:首先利用动态神经网络对系统进行辨识,然后在辨识估计基础上设计控制器将混沌状态引导至期望目标位置;并且对系统的稳定性能进行了严格数学分析;Duffing方程的数值仿真实验证明了所提出方法的有效性。     

基于T-S模型的混沌保密通信系统设计

基于T-S模型讨论了混沌系统的鲁棒同步问题,模糊控制器对于混沌系统本身受到的外界扰动具有一定的鲁棒性能,并将该方法应用于基于混沌同步的保密通信系统设计,实现了对数字图像的保密通信。通过对离散Henon混沌系统的仿真,证实了该方法的有效性。