Adaptive function Q‐S synchronization of chaotic systems with unknown parameters

This work investigates the adaptive function Q‐S synchronization of non‐identical chaotic systems with unknown parameters. The sufficient conditions for achieving Q‐S synchronization with a desired scaling function of two different chaotic systems (including different dimensional systems) are derived based on the Lyapunov stability theory. By the adaptive control technique, the control laws and the corresponding parameter update laws are proposed such that the Q‐S synchronization of non‐identical chaotic systems is to be achieved. Finally, four illustrative numerical simulations are also given to demonstrate the effectiveness of the proposed scheme. Copyright © 2009 John Wiley & Sons, Ltd.     

具有传输通道时间延迟的一类混沌系统脉冲控制同步

针对一类混沌系统同步控制问题,利用脉冲微分方程的稳定理论,研究了传榆信号具有时间延迟的混沌系统脉冲同步问题,给出了两个混沌系统实现全局渐进同步的判据方法。该方法仅采用具有时间延迟的驱动系统与响应系统输出偏差的线性反馈作为脉冲控制信号,驱动两个混沌系统达到全局渐进同步,且适用于绝大多数混沌系统的同步控制。所设计的控制器结构简单,收敛速度快,易于实现。Roessler混沌系统的仿真实验进一步验证了该方法的有效性和可行性。     

Composite learning fuzzy synchronization for incommensurate fractional‐order chaotic systems with time‐varying delays

This paper presents a composite learning fuzzy control to synchronize two different uncertain incommensurate fractional‐order time‐varying delayed chaotic systems with unknown external disturbances and mismatched parametric uncertainties via the Takagi‐Sugeno fuzzy method. An adaptive controller together with fractional‐order composite learning laws is designed based on both a parallel distributed compensation technology and a fractional Lyapunov criterion. The boundedness of all variables in the closed‐loop system and the Mittag‐Leffler stability of tracking error can be guaranteed. T‐S fuzzy systems are provided to tackle unknown nonlinear functions. The distinctive features of the proposed approach consist in the following: (1) a supervisory control law is designed to compensate the lumped disturbances; (2) both the prediction error and the tracking error are used to estimate the unknown fuzzy system parameters; (3) parameter convergence can be ensured by an interval excitation condition. Finally, the feasibility of the proposed control strategy is demonstrated throughout an illustrative example.     

An optimal approach to synchronize non‐identical chaotic circuits: An experimental study

The control signal magnitude and energy are among the limiting and therefore important factors to be addressed in the practical applications of a synchronization scheme. In this paper, we present an algorithm to find control parameters in an active sliding mode controller in order to reduce the control effort in synchronizing non‐identical chaotic systems. We also determine uncertainties bound on the systems dynamics for which the calculated control parameters still guarantee the occurrence of the sliding motion of the error states. The proposed controller was practically applied on an experimental setup, consisting of two chaotic circuits, which resembles Chen and Lu systems behavior. Experimental results confirm our theoretical reasoning as well as the effectiveness of the proposed control design technique. Copyright © 2010 John Wiley & Sons, Ltd.     

七阶混沌振荡电力系统的自耦PD控制

为了抑制七阶电力系统中的混沌振荡,根据自耦PID控制理论提出了一种简单的混沌控制方法。该方法首先将七阶混沌系统控制问题分解为三个严格反馈子系统的控制问题,然后将每个子系统已知和未知动态分别定义为一个总扰动,进而将三个子系统等价映射为一个三阶线性扰动系统和两个二阶线性扰动系统。据此分别构建了在总扰动反相激励下的三个受控误差系统。根据自耦PID控制理论,分别设计了一个扩展自耦PD控制器和两个自耦PD控制器。最后分析了每个子系统的鲁棒稳定性和抗扰动鲁棒性。仿真结果验证了所提控制方法的有效性,每个状态变量均能由混沌振荡状态恢复到稳定运行状态,且控制信号光滑。因此该方法在电力混沌振荡控制系统领域具有良好的实际应用前景。     

存在扰动的永磁同步电机混沌运动模糊自适应同步

电机的混沌运动并不总是有害的,在某种特殊应用场合中永磁同步电机的混沌运动是有益的,因此需要对永磁同步电机的混沌运动进行反控制。提出了一种存在扰动的永磁同步电机（PMSM）混沌运动的模糊自适应同步控制方法。分析了PMSM混沌运动的吸引子和lyapunov指数谱,使模糊控制规则满足系统的lyapunov稳定条件,设计模糊自适应控制器对存在扰动的PMSM混沌系统进行同步控制,仿真结果表明该方法可实现PMSM混沌运动的同步控制,具有较好的控制效果。     

Fixed time synchronization of delayed chaotic neural networks by using active adaptive control

This article aims to investigate the fixed time synchronization of a class of chaotic neural systems by way of adaptive control method. Using Lyapunov stability theory, a new fixed time stability theorem which plays an important role on the synchronization scheme is presented at first. Then, combining the fixed time stability theorem and adaptive control technique, an adaptive control scheme has been developed to achieve the fixed time synchronization of chaotic neural systems. The proposed controllers assure the global convergence of the error dynamics in fixed-time based on the Lyapunov stability theory. Furthermore, the proposed control strategy cannot only provide a fast convergence rate, but also afford a bounded convergence time which is unrelated to the initial values and easy to work out by using the simple time calculation formula. Finally, numerical simulations are presented by taking a typical two-order chaotic neural system as an example to verify and demonstrate the effectiveness of the proposed scheme.     

Adaptive actuator failure compensation design for unknown chaotic multi‐input systems

In this paper, an adaptive control approach is designed for compensating the faults in the actuators of chaotic systems and maintaining the acceptable system stability. We propose a state‐feedback model reference adaptive control scheme for unknown chaotic multi‐input systems. Only the dimensions of the chaotic systems are required to be known. Based on Lyapunov stability theory, new adaptive control laws are synthesized to accommodate actuator failures and system nonlinearities. An illustrative example is studied. The simulation results show the effectiveness of the design method. Copyright © 2014 John Wiley & Sons, Ltd.     

Adaptive switching control of uncertain fractional systems: Application to Chua's circuit

Since the introduction of fractional‐order differential equations, there has been much research interest in synthesis and control of oscillatory, periodic, and chaotic fractional‐order dynamical systems. Therefore, in this article, the problem of stabilization and control of nonlinear three‐dimensional perturbed fractional nonlinear systems is considered. The major novelty of this article is handling partially unknown dynamics of nonlinear fractional‐order systems, as well as coping with input saturation along the existence of model variations and high‐frequency sensor noises via just one control input. The method supposes no known knowledge on the upper bounds of the uncertainties and perturbations. It is assumed that the working region of the input saturation function is also unknown. After the introduction of a simple finite‐time stable nonlinear sliding manifold, an adaptive control technique is used to reach the system variables to the sliding surface. Rigorous stability discussions are adopted to prove the convergence of the developed sliding mode controller. The findings of this research are illustrated using providing computer simulations for the control problem of the chaotic unified system and the fractional Chua's circuit model.     

Rossler系统的混沌控制

根据Rossler系统的动力学方程,数值仿真了系统随自身参数变化的全局分岔图,分析了参数变化引起系统动力学行为的变化。针对系统混沌状态,分别用自适应控制法和控制法两种方法对系统进行控制,仿真结果显示:两种控制法均能将系统控制在稳定的周期轨道。对比了两种控制法对系统控制的结果,在自适应控制中,随着控制参数逐步减小,系统由单周期运动经倍化分岔为双周期运动,再经倍化分岔序列最终通向混沌,动力学行为规则,对应控制参数选择区域连续;在控制中,系统由混沌状态转变为三周期运动,随着控制参数逐步增大,周期运动发生倍化分岔,再经倍化分岔序列通向混沌,系统动力学行为丰富,对应控制参数选择区域范围明确。为Rossler系统的动力学行为研究和混沌控制提供了理论支持,为Rossler系统在工程领域的应用及控制提供了参数选择区域,为其它系统的混沌控制及动力学行为研究提供了经验和方法。     

一种电流模式Buck-Boost变换器的混沌与反混沌混合控制方法*

由于混沌系统具有内在随机性的特征,其状态变量之间的关联性有时很弱,甚至不相关,因而难以对系统实施有效控制。本文基于状态关联和参数扰动的思想提出了一种Buck-Boost变换器混沌与反混沌混合控制方法。该方法首先定义一个调整系数来表征状态变量之间的耦合强度,通过调节该系数达到控制其耦合强度的目的,并建立系统的数学模型。然后利用系统的微分项来表征参数扰动项,对系统施加一定范围的参数扰动。最后根据控制目标,通过改变调整系数实现对系统的混沌与反混沌控制。基于单值矩阵理论和Simulink仿真平台验证了方法的有效性。该方法仅需调整一个外部参数,即可将任意状态下的电流型Buck-Boost变换器控制到周期1、2轨道及混沌态。     

不确定混沌电力系统的鲁棒自适应跟踪控制

针对混沌电力系统的跟踪控制问题,在考虑系统含有常参数不确定性及未知干扰的前提下,采用动态面控制方法,设计了鲁棒自适应跟踪控制器,保证了闭环系统的半全局渐近稳定,进而使输出渐近跟踪参考轨迹.理论分析及仿真结果表明,所设计的自适应非线性控制器能够有效抑制简单电力系统的混沌振荡,且具有一定的适应性及鲁棒性.     

Observers for a Class of Chaotic Systems

The design of observers for a class of practical physical chaotic systems is discussed. By using only one state variable and its time derivatives, a control law is constructed to achieve the synchronization between the investigated chaotic systems and their observers, and the results are proved theoretically. Several observers of chaotic systems are designed by using this method. Translated from “Observers for a Class of Chaotic Systems” published in Journal of Southwest China Normal University (Natural Science), 2004, 29(1): 53–57 (in Chinese)     

The online parameter identification of chaotic behaviour in permanent magnet synchronous motor by Self-Adaptive Learning Bat-inspired algorithm

One of the main issues in engineering is the identification of nonlinear systems. Because of the complicated as well as unexpected behaviours of these chaotic systems, it is introduced as special nonlinear systems. A minute change in the primary conditions of such systems would lead to significant variations in their behaviours. On the other hand, due to simple structure of Permanent Magnet Synchronous Motors (PMSM) and its high applications in industry, the use of this machine is dramatically increasing these days. The reflection of a chaotic behaviour as the Permanent Magnet Synchronous Motor is positioned in a particular area. In the model of PMSM, the exact parameters of the system are required to properly control and spot the error. In this paper, Self-Adaptive Learning Bat-inspired Optimization algorithm is used for solving both offline and online parameter estimation problems for this chaotic system. In addition, noise is considered as one of influential factors in control of PMSM. According to simulation results, it can be claimed that the proposed algorithm is a very powerful algorithm for online parameter identification for PMSM.     

不确定混沌系统的鲁棒自适应容错同步控制

针对一类带有执行器故障、非线性不确定性以及外界干扰的混沌系统,设计一个鲁棒自适应容错控制器,来实现主从混沌系统之间的同步容错控制。不需要知晓准确的故障信息以及外界干扰的上界,根据自适应律在线估计未知量。结合自适应控制技术,设计鲁棒自适应容错控制器,使得无论执行器是否有故障发生,主从两个混沌系统都能够实现同步。以经典的蔡氏混沌电路系统为例进行数值仿真,仿真结果验证了所设计控制器的有效性和可行性。     

Chaotification of unknown linear and nonlinear systems with applications

A new chaotification method (chaos anti-control) of dynamical systems, which have unknown parameters, is proposed in this paper. The method is based on tracking reference models, through a control law that chaotifies a class of non-linear systems, linear in the control and fully state feedback linearizable. Besides, adaptive laws for control parameters are derived that guarantee the stability of the resulting adaptive system and the convergence of the tracking error to zero. The proposed method has two possible approaches: indirect and direct. Finally, the proposed scheme is applied to secure communications, by means of encrypted information transmission and reception of a message in a chaotic system.     

Adaptive control of complex systems with unknown dynamics and input constraint: Applied to a chaotic elastic beam

Owing to the limitations of system identification and modeling techniques, there is usually some unknown dynamics in the mathematical models of the complex systems. In addition, external perturbations can affect the chaotic systems' responses and may destroy the desired control purpose. Consideration of such uncertain dynamics and external fluctuations in control applications is important in research and practice. On the other hand, because of the limited operation of control actuators, most of the practical implementations of control systems are forced with some input constraints. Therefore, this paper investigates the control problem of uncertain autonomous and/or nonautonomous complex chaotic systems in the presence of input saturation. The upper bounds of the unknown dynamics, modeling uncertainties, external perturbations, and the parameters of the saturation function are assumed to be unknown in advance. To make a fast control response, an adaptive nonsingular terminal variable structure controller is proposed to assure the finite‐time stability of the equilibrium states. Rigorous stability analysis is performed to prove the correct performance of the designed control algorithm. Numerical simulations on the unified system and a chaotic elastic beam model are developed to demonstrate the usefulness of the introduced adaptive control strategy. It is worth to notice that the derived adaptive nonsmooth sliding mode approach is general and it can be easily adopted for controlling of a wide class of uncertain MIMO nonlinear systems.     

Suppressing harmonics in four‐quadrant AC‐DC converters with chaotic SPWM control

In this paper, a new chaotic sinusoidal pulse width modulation (chaotic SPWM) control is proposed and implemented in a four‐quadrant AC‐DC converter for harmonics suppression, where a chaotic carrier plays a key role. Further, the relationship of the harmonic distribution and carrier frequency is derived by analyzing the harmonic components of the AC‐DC converter, which is useful for revealing the operation principle of the chaotic SPWM control for harmonic suppression. Finally, the simulation and experimental results illustrate the effectiveness of the proposed chaotic SPWM control on harmonics reduction. Copyright © 2012 John Wiley & Sons, Ltd.     

开关电感Boost变换器的失效机理及基于参数扰动的混沌控制方案研究

开关电感Boost变换器是新能源系统中应用较为广泛的一种高增益DC-DC变换器。由于变换器本身的特性,当电路参数的变化超出一定范围时,会发生分岔、混沌等非线性现象,造成变换器失效,此时变换器无法正常稳定运行并且工作性能下降,因此有必要控制变换器从混沌态重回稳定态。基于参数扰动混沌控制法的基本原理,设计了适用于峰值电流控制型开关电感Boost变换器的混沌控制方案。该方案可使工作于混沌状态的变换器能迅速返回周期-1态稳定工作,其输出电压增益得以提高、输出纹波显著降低,并且在输入和负载有较大扰动时变换器系统均能稳定工作。利用非线性理论对变换器失效机理进行分析和混沌控制,对于DC-DC变换器参数设计、稳定性分析和性能提升具有一定的实际应用价值。     

Chaotic self-adaptive differential harmony search algorithm based dynamic economic dispatch

Dynamic economic dispatch (DED) is one of the main optimization problems in electrical power system operation and control. DED problem is a non-smooth and non-convex problem when valve point effect, ramp-rate limits and prohibited operating zones of generation units are taken into account. This paper proposes an efficient chaotic self-adaptive differential harmony search (CSADHS) algorithm to solve the complicated DED problem in the presence of valve point effect, ramp-rate limits and prohibited operating zones constraints. In the proposed algorithm, chaotic self-adaptive differential mutation operator is used instead of pitch adjustment operator in the harmony search (HS) algorithm, to enhance the searching performance to find the quality solution. The effectiveness of the proposed algorithm is demonstrated on 10, 15 and 30 unit systems for a period of 24 h. The simulation results obtained by the proposed algorithm are compared with the results obtained, using differential harmony search (DHS) algorithm, chaotic differential harmony search (CDHS) algorithm, and also with the results of other methods available in the literature. In terms of solution quality, the proposed algorithm is found to be better than other algorithms and in terms of speed of convergence, standard deviation of generation cost, and computational time, the proposed algorithm is better than DHS and CDHS algorithm.