超混沌复系统的自适应广义组合复同步及参数辨识

该文针对含未知参数的异结构超混沌复系统,基于自适应控制及Lyapunov稳定性理论,提出一种新的自适应广义组合复同步方法 (GCCS)。首先给出广义组合复同步的定义,将驱动-响应系统的同步问题转化为误差系统零解的稳定性问题;然后从理论上设计了非线性反馈同步控制器及参数辨识更新律,并引入误差反馈增益,以控制同步的收敛速度;最后以超混沌复Lorenz系统、超混沌复Chen系统、超混沌复L系统的广义组合复同步与参数估计为例,从数值仿真角度验证了所提方法的正确性和有效性。     

Chaos Synchronization in Complex Networks

In this paper, we study chaos synchronization in complex networks with time-invariant, time-varying and switching configurations based on the matrix measure of complex matrices. To begin with, we propose an analytical condition for chaos synchronization in complex networks with a time-invariant configuration. Secondly, we obtain some less conservative synchronization conditions for networks with a time-varying configuration. Thirdly, we consider chaos synchronization in networks with time-average and switching configurations. If complex subnetworks satisfy certain conditions, the networks with time-average and switching configurations are $M$-synchronizable. At last, we analyze the nonsynchronizability of complex networks. Chaos synchronization in complex networks can't be realized if the coupling configuration and the inner-coupling matrix satisfy certain conditions. Theoretical analysis and numerical simulations verify the effectiveness of the proposed synchronization criteria.      

两个带有已知或未知参数的复杂网络的改进函数投影同步

近年来复杂网络在科学与工程各个领域受到了广泛关注,其中复杂网络同步问题是复杂网络研究的热点之一。该文研究两个复杂网络实现改进函数投影同步的方法。分别基于复杂网络模型参数已知和未知两种情况,利用李雅普诺夫稳定性理论和自适应控制技术,设计自适应同步控制器,使两个复杂网络达到改进函数投影同步。最后分别基于这两种情况利用数值仿真验证所提方法的有效性。     

Adaptive Feedback Synchronization of a General Complex Dynamical Network With Delayed Nodes

In the past decade, complex networks have attracted much attention from various fields of sciences and engineering. Synchronization is a typical collective behavior of complex networks that has been extensively investigated in recent years. To reveal the dynamical mechanism of synchronization in complex networks with time delays, a general complex dynamical network with delayed nodes is further studied. Based on a suitable model, we investigate the adaptive feedback synchronization and obtain several novel criteria for globally exponentially asymptotic synchronization. In particular, our hypotheses and the proposed adaptive controllers for network synchronization are very simple and can be readily applied in practical applications. Finally, numerical simulations are provided to illustrate the effectiveness of the proposed synchronization criteria.     

系统参数不同的简并光学参量振荡器之间的混沌同步

简并光学参量振荡器系统在一定的参数下可出现混沌、周期或准周期状态,利用参数自适应控制和反馈控制技术实现了不同系统参数的两个简并光学参量振荡器混沌同步、周期或准周期同步,给出了参数自适应控制律和反馈控制函数的具体形式,并给出了同步的严格数学理论证明。     

Adaptive Synchronization of Complex Dynamical Networks with Time-Varying Delays

This paper addresses the problem of adaptive pinning synchronization of complex dynamical networks with nonlinear delayed intrinsic dynamics and time-varying delays. By introducing decentralized adaptive strategies to both the coupling strengths and the feedback gains, it is proved that the complex dynamical network can synchronize with the desired state for the bounded time-varying delays even when only one node is informed, without any global information of the underlying network. Finally, some numerical simulations are given to verify the main results and show the superiority of these self-designed adaptive strategies.     

Effect of Mismatched Loop Delay in Continuous-Time Complex Sigma-Delta Modulators

Continuous-time (CT) complex $SigmaDelta$ modulators seriously suffer from delay in real and imaginary feedback paths. The mismatched loop delay results in a degradation of the signal-to-noise ratio. In this paper, analytical considerations of mismatched loop delay in CT complex $SigmaDelta$ modulators are presented. Discrete-time equivalent transfer functions to that of a CT complex loop filter are derived from continuous-discrete transformation in the complex signal domain. A solution for reducing or compensating the effect of mismatched loop delay is proposed.      

基于滑动相关峰检测的混沌码同步法

混沌无线数字通信是未来高安全高保密无线通信的重要发展方向,而混沌码同步是其核心技术之一。该文根据混沌无线通信特点,提出一种基于滑动相关峰检测的混沌码同步方法。针对非周期混沌码同步,设计了在混沌码同步3个约束条件下的相位延迟控制模块,搭建了基于Logistic序列的同步系统动态模型,并进行了仿真。仿真结果表明,该方法可实现收发两端混沌码同步,同步速度快,抗噪能力强,有效地解决了混沌无线数字通信中的同步方法问题。     

一类新型超混沌系统的非线性反馈同步研究

一类由快变和慢变吸引子构成的新型超混沌系统,具有强的抗噪声能力,但是采用传统同步算法时,同步收敛速度较慢,同步性能对响应系统参数敏感。针对该问题,该文提出非线性反馈同步算法,根据Hurwitz稳定原理,设计非线性控制变量,使得误差方程雅可比矩阵的特征值实部均小于零,并使得特征值的绝对值较大。该算法比传统同步算法收敛速度快,并且具有对系统参数不敏感的优点。仿真结果验证了上述算法的有效性。     

Adaptive Stabilization and Synchronization for Chaotic Lur'e Systems With Time-Varying Delay

In this paper, we propose an adaptive scheme for the stabilization and synchronization of chaotic Lur'e systems with time-varying delay. Based on the invariant principle of functional differential equations, the strength of the feedback controller is enhanced adaptively to stabilize and synchronize chaotic Lur'e systems. The derivative-constraint that the time-varying delay is required to be differentiable and its derivation is less than one can be removed by using LaSalle-Razumikhin-type theorems. The time-varying delay is allowed to be bounded without any additional constraint or unbounded with derivative-constraint. This method is analytical, rigorous and simple to implement in practice. In addition, it is quite robust against the effect of parameters uncertainty and noise. Two examples are provided to show the effectiveness of the proposed scheme. The results of the paper demonstrate the fruitfulness of the modern feedback and adaptive control theory application to the stabilization and synchronization problems for delayed chaotic systems.     

Chaos synchronization and chaotic signal masking in semiconductor lasers with optical feedback

Theoretical and experimental investigations of chaos synchronization and its application to chaotic data transmissions in semiconductor lasers with optical feedback are presented. Two schemes of chaos synchronization-complete and generalized synchronization-are discussed in the delay differential systems. The conditions for chaos synchronization in the systems and the robustness for the parameter mismatches are studied. The possibility of secure communications based on the chaos masking technique in semiconductor lasers with optical feedback is also discussed, and message transmission of a 1.5-GHz sinusoidal signal is demonstrated. The method of bandwidth enhancement of chaotic carriers is proposed for broad-band chaos communications.     

A State-Observer-Based Approach for Synchronization in Complex Dynamical Networks

In this paper, a new approach for synchronization of complex dynamical networks is proposed based on state observer design. Unlike the common diagonally coupling networks, where full state coupling is typically needed between two nodes, here it is suggested that only a scalar coupling signal is required to achieve network synchronization. Some conditions for synchronization, in the form of an inequality, are established based on the Lyapunov stability theory, which can be transformed to a linear matrix inequality and easily solved by a numerical toolbox. Two typical dynamical network configurations, i.e., global coupling and nearest-neighbor coupling, with each node being a modified Chua's circuit, are simulated. It is demonstrated that the proposed scheme is effective in achieving the expected chaos synchronization in the complex network     

AdaSynch: A General Adaptive Clock Synchronization Scheme Based on Kalman Filter for WSNs

Efficient and accurate clock synchronization is a challenge for wireless sensor networks (WSNs). Unlike previous works on clock synchronization in WSNs that consider communication delay as the main cause of clock inaccuracy, we propose a new adaptive synchronization scheme, AdaSynch, which considers the principium of the clock. We aim to overcome the challenges posed by WSNs’ resource constraints such as limited energy and bandwidth, low precision oscillators and random factors. By implementing some experiments on TelosB platform, we find that the clock system switches between multiple clock models. Motivated by experiment results, we establish a general clock model which describes the clock offset in terms of the oscillators. We then design two kinds of basic Kalman filter models to achieve clock synchronization. In order to execute Kalman filtering, we propose a recursion method based on the Expectation-Maximization (EM) algorithm to access the parameters of the Kalman filter model adaptively. To describe alternation in the clock model, we propose a Multimodel Kalman filter, and put forward an adaptive method based on hypothesis testing to describe these complexities in the clock model. We demonstrate the performance gains of our scheme through experiments using different Kalman filter models based on experiment data.     

双光反馈半导体激光混沌高复杂度优化分析

基于排列熵(PE)分析,提出了一种基于半导体激光器(SL)在双光反馈作用下获取高复杂度混沌激光的方案。仿真结果表明,当两个光反馈的延迟时间近似相同、而差值约为激光器弛豫振荡周期一半时,混沌光的PE特征值达到最大,具有最高的复杂度。调节双光反馈的强度值,混沌光的PE特征值将随反馈强度的增加而首先快速增大,然后再缓慢降低。在一定优化双光反馈强度值范围内,PE特征值可取得最大值,从而得到高复杂度的混沌光输出。与单光反馈SL系统相比较,在不同反馈强度下,双光反馈系统所获得的混沌光的PE特征值也总是大于单光反馈系统的结果。     

New Synchronization Stability of Complex Networks With an Interval Time-Varying Coupling Delay

In this brief, the problem of synchronization stability analysis for complex dynamical networks with a time-varying coupling delay is studied. The delay considered in this brief is assumed to vary over an interval where the lower and upper bounds are known. By dividing the interval time-varying delay into a constant and a time-varying part and using a delay-partitioning approach, a new Lyapunov-Krasovskii functional is constructed. Based on this, a new delay-range-dependent criterion is obtained in terms of linear matrix inequalities. A numerical example is provided to show the effectiveness of the proposed results.     

Characteristics of chaos synchronization in semiconductor lasers subject to polarization-rotated optical feedback

We numerically investigate the detailed characteristics of chaos synchronization in semiconductor lasers subject to polarization-rotated optical feedback. The emission of the dominant TE mode of a drive laser is rotated 90 deg and fed back to the laser with time delay. The polarization-rotated TE mode is also injected with time delay into the TM mode of a second laser. Two types of synchronization with different time-lags are found, as in the case for synchronization in semiconductor lasers with nonrotated optical feedback. However, a significant difference to the nonrotated optical feedback case is that neither of the two types of synchronization requires matching of optical carrier frequency between the two lasers.     

Pinning a Complex Delayed Dynamical Network to a Homogenous Trajectory

Time delay exists in many fields, such as biology, neural network, mechanics, ecology, and so on. It is important for us to investigate the control of interconnected time-delay systems. In this brief, we propose two schemes to pin a complex delayed dynamical network to a homogenous trajectory. In particular, we prove that the delayed dynamical network is asymptotically synchronized with linear feedback control, and it is exponentially asymptotically synchronized with adaptive feedback controllers. We also find that the number of pinned nodes satisfies an inequality for synchronization. Additionally, the coupling matrix is not necessarily symmetric, and the pinned nodes can randomly be selected. Moreover, the linear feedback gain need not be large. Finally, two well-known network models are provided as illustrative examples to confirm the effectiveness of the technique.     

On Designing Time-Varying Delay Feedback Controllers for Master–Slave Synchronization of Lur'e Systems

This paper is concerned with the problem of designing time-varying delay feedback controllers for master-slave synchronization of Lur'e systems. Two cases of time-varying delays are fully considered; one is the time-varying delay being continuous uniformly bounded while the other is the time-varying delay being differentiable uniformly bounded with the derivative of the delay bounded by a constant. Based on Lyapunov-Krasovskii functional approach, some delay-dependent synchronization criteria are first obtained and formulated in the form of linear matrix inequalities (LMIs). The relationship between synchronization criteria for the two cases of time-varying delays is built. Then, sufficient conditions on the existence of a time-varying delay feedback controller are derived by employing these newly-obtained synchronization criteria. The controller gains can be achieved by solving a set of LMIs. Finally, Chua's circuit is used to illustrate the effectiveness of the design method.     

非耗散耦合复杂网络受控同步能力分析

该文研究了非耗散耦合网络的受控同步能力问题。在分析非耗散耦合网络外耦合矩阵特征值分布规律的基础上,给出了非耗散耦合网络的同步控制律。发现外耦合矩阵最大最小特征值之差越小,网络受控同步能力越强,耦合强度越小,网络越有可能通过控制取得同步,但在某些情况下所需要的控制增益绝对值也越大。最后以Lorenz振子小世界网络在混沌轨道上的同步为例对相关结论的有效性进行了验证。     

压电振子复参数等效电路模型研究

为得到压电振子精确的等效电路,将等效电路参数设为复数,即每一电路元件参数包含实部和虚部两部分,其中实部部分意义与传统参数意义相同,而虚部部分表示相应的机械、介电及压电损耗。为得到等效电路参数,给出了等效电路参数与压电材料参数之间相互关系。通过仿真和实验两种方法对复数模型与传统模型进行了性能比较,验证了复数等效电路模型的有效性和精确性。