凹槽滤波反馈控制混沌系统

通过对具有扰动作用的平面Hamilton混沌动力系统增加一线性的反馈控制器———凹槽滤波器, 基于Melnikov方法这一混沌的微扰判据给出合适的反馈控制器参数, 引导系统从混沌运动转化为期望的低周期运动, 并采用平均理论作了稳定性分析. 数值仿真结果将进一步证实本文的结论.     

利用正反馈引导混沌系统到周期解

提出了一种抑制混沌的方法, 通过对混沌动力系统增加一个基于系统变量的正反馈控制项, 成功而快速引导系统从混沌运动转化为低周期运动. 利用Melnikov方法分析了该控制方法在Duffing振子中实现混沌抑制的控制机理, 得到了结论: 正反馈项可以消除混沌系统的稳定流形和不稳定流形的横截相交. 仿真表明, 该方法简单而广泛适用.     

Converting chaos into periodic motion by state feedback control

A simple control method is presented to convert chaos into periodic motion by using linear state feedback of an available system variable. The low-periodic orbits can be derived from the chaotic attractor with slight change of the dynamical structure in the original dynamics. Melnikov's perturbation method in generalized Hamiltonian systems is introduced to explain the control mechanism of directing chaotic motion towards low-periodic motion in the Lorenz equations. Moreover, the existence of periodic orbits is examined in the perturbed Lorenz system. Simulation results verify the effectiveness of Melnikov's analysis.     

Simple feedback systems with chaotic behaviour

An example is given of a second-order dynamical system, containing a relay with hysteresis, which can display chaotic motion. It is shown that this system can be approximated by a third-order model with a continuous non-linearity, which appears to behave in a similar manner.     

混沌Lorenz系统延迟反馈控制的机理分析

利用广义Hamilton系统理论的Melnikov方法,严格分析了延迟反馈方法控制混沌Lorenz系统到周期解的机理,揭示了延迟时间与控制混沌的关系.延迟反馈项实际上是一个作用明显的扰动项,通过选择合适的参数,使得系统的稳定流形与不稳定流形不再横截相交,Smale意义下的混沌受到抑制,将Lorenz混沌系统引导到各种不同的周期轨道;可见,延迟时间关系到控制扰动量的大小,但不必是混沌吸引子内嵌不稳定周期轨道的周期整数倍.另外,通过数值仿真,其结果与理论分析相符,从而表明了该分析方法的有效性.     

Robust synchronization of chaotic systems using slidingmode and feedback control

We propose a robust scheme to achieve the synchronization of chaotic systems with modeling mismatches and parametric variations. The proposed algorithm combines high-order sliding mode and feedback control. The sliding mode is used to estimate the synchronization error between the master and the slave as well as its time derivatives, while feedback control is used to drive the slave track the master. The stability of the proposed design is proved theoretically, and its performance is verified by some numerical simulations. Compared with some existing synchronization algorithms, the proposed algorithm shows faster convergence and stronger robustness to system uncertainties.     

Extended Chen: a new class of chaotic fractional-order systems

A new class of chaotic fractional-order systems is introduced and its necessary conditions for chaotic behaviour of this class have been provided. These chaotic systems are constructed based on the extension of fractional-order chaotic Chen system by addition of a general function term, satisfying some necessary conditions. This property makes the chaotic behaviour of the extended system, to large extent, independent of the selected function and so a vast range of chaotic systems can be synthesized. The main application of the proposed chaotic systems may be in secure communication systems. To make the subject clearer and in order for validation of the proposed model, five examples are provided and their results are simulated. The results confirm the theoretic analyses very well.     

Chaos control and hybrid projective synchronization for a class of new chaotic systems

The problems on chaos control and hybrid projective synchronization for a class of new chaotic systems are considered. First, new 4D chaotic systems are proposed by introducing an additional state into a 3D quadratic chaotic system and the states of the systems corresponding to the different ranges of parameter b are exhibited. Second, a single scalar adaptive feedback controller for chaos control of the systems is presented. Third, hybrid projective synchronization (HPS) of two of the chaotic systems with parameters in different conditions are investigated by presenting adaptive feedback control strategies with adaptive parameter update laws and considering controller simplification to achieve complete synchronization. Finally, numerical simulations are demonstrated to verify the effectiveness of the strategies.     

一类非线性时滞互联系统模糊分散输出反馈控制

对于一类状态不可测非线性互联时滞系统,给出一种基于观测器的模糊分散输出反馈控制方法.首先采用模糊T-S模型对非线性互联时滞系统进行模糊建模,在此基础上给出了模糊分散观测器和基于观测器的模糊分散输出控制器的设计.应用李亚普诺夫函数法和线性矩阵不等式方法给出了模糊分散控制系统稳定的充分条件.仿真结果进一步验证了所提出的模糊分散控制方法的有效性.     

Adaptive output control of a class of uncertain chaotic systems

In this paper, a new observer-based backstepping output control scheme is proposed for stabilizing and controlling a class of uncertain chaotic systems. The controller is designed through the use of a robust observer and backstepping technique. We firstly show that many chaotic systems as paradigms in the research of chaos can be transformed into a class of nonlinear systems in the feedback form. Secondly, the synchronization problem is converted to the tracking problem from control theory, thereby leading to the use of state observer design techniques. A new observer is utilized to estimate the unmeasured states. Unlike some existing methods for chaos control, no priori knowledge on the system parameters is required and only the output signal is available for control purpose. The Lyapunov functions are quadratic in the state estimates, the observer errors and the parameter estimation error based on the backstepping technique. It is shown that not only global stability is guaranteed by the proposed controller, but also both transient and asymptotic tracking performances are quantified as explicit functions of the design parameters so that designers can tune the design parameters in an explicit way to obtain the desired closed-loop behavior.     

基于模型的输出反馈网络控制系统反馈调度研究

针对基于模型的网络控制系统缺乏应对动态变化的网络负载问题,设计反馈调度器,依据实际的网络拥塞情况,调整基于模型的网络控制系统的状态更新时间.为应对状态不完全可测的情况,在控制结构中使用了状态观测器,并证明了所提出系统在可变更新时间情况下的稳定性.仿真结果验证了稳定性条件的正确性和新网络控制系统结构的有效性.     

Measurement feedback control for a class of feedforward nonlinear systems

We propose a measurement feedback controller for a class of feedforward nonlinear systems under sensor noise. The sensor noise has unknown magnitude, frequency, and phase. Our proposed controller is coupled with a low‐pass filter in such a way that the sensor noise is attenuated. We show that the controlled system results in bounded states whose ultimate bounds are inversely proportional to the minimum frequency of the sensor noise. Our result is further generalized to work in a case where the sensor noise is only required to have a Fourier transform with finite energy. Moreover, if the sensor noise enters only at partial states, depending on the location of the sensor noise, the ultimate bounds of the particular states can be made arbitrarily small via the gain factor of the controller. Copyright © 2012 John Wiley & Sons, Ltd.     

一类离散混沌系统的传输受限同步问题

研究了一类离散混沌系统信息受限条件下的同步问题.将具有离散形式的混沌驱动系统和具有控制输入的响应系统通过一个有限容量信道的通讯网络进行连接.在这种情况下,设计了合适的编解码方法使得传输误差在一定的条件下达到渐近稳定.同时,在线性矩阵不等式条件下,获得了同步误差方程关于传输误差是输入状态稳定,从而实现了混沌系统在信道容量有限条件下的完全同步.最后,通过Fold混沌系统验证了本文方法的有效性.     

On tracking control of a class of complementary-slackness hybrid mechanical systems

In this note we consider the problem of feedback control of n-dof (degree-of-freedom) rigid manipulators subject to a scalar frictionless unilateral constraint is the vector of generalized coordinates). The stability analysis relies on a stability concept that incorporates the hybrid and nonsmooth dynamical feature of the overall system. It is shown that stability of the closed-loop system can be obtained. This work generalizes the results in [Brogliato et al. (IEEE Trans. Automat. Control 42(2) (1997) 200–215)] which were mainly restricted to the 1-dof case. It also clarifies some concepts related to the hybrid nature of closed-loop complementary-slackness mechanical systems.     

一类网络控制系统的稳定性分析

针对网络控制系统中普遍存在的信息量化问题,采用基于模型的控制策略,研究了一类网络控制系统的稳定性.在考虑均匀量化的影响下,对于不同的初始量化误差,分别讨论了系统的稳定性,并给出了保证系统全局指数稳定的充分必要条件以及系统的稳定域范围.仿真结果验证了所得结论的正确性.     

A control design method for a class of switched linear systems

In this note we consider the stability properties of a system class that arises in the control design problem of switched linear systems. The control design we are studying is based on a classical pole-placement approach. We analyse the stability of the resulting switched system and develop analytic conditions which reduce the complexity of the stability problem. We further consider two special cases for which strongly simplified conditions are obtained that support the analytic controller design.     

Adaptive backstepping control and synchronization of a modified and chaotic Van der Pol-Duffing oscillator

In this paper,we propose a backstepping approach for the synchronization and control of modified Van-der Pol Duffing oscillator circuits.The method is such that one controller function that depends essentially on available circuit parameters that is sufficient to drive the two coupled circuits to a synchronized state as well achieve the global stabilization of the system to its regular dynamics.Numerical simulations are given to demonstrate the effectiveness of the technique.     

一类非线性系统的模糊自适应滑模输出反馈控制

针对一类非线性系统，提出一种新的模糊自适应滑模输出反馈控制方法，该方法不需要非线性系统的状态可测的假设。基于李亚普诺夫函数方法，给出了模糊自适应输出反馈控制律以及在线调节的参数自适应律，证明了模物闭环系统的稳定性和跟踪误差的收敛性。     

包含SVC和非线性负荷的电力系统耗散实现与控制

采用Hamilton函数方法研究了包含静止无功补偿器(SVC)和非线性负荷的电力系统的反馈控制问题. 首先建立了系统的非线性微分代数方程模型, 通过预置状态反馈完成了耗散Hamilton实现. 然后利用该耗散实现结构,通过阻尼注入方式设计了基于能量的SVC非线性控制器. 本文所设计的控制器结构简单, 物理意义明确. 仿真结果表明该控制器能有效提高电力系统的暂态稳定性.