Pinning Cluster Synchronization of Coupled Nonidentical Harmonic Oscillators Under Directed Topology

This paper addresses cluster synchronization of coupled harmonic oscillators over directed fixed and switching topologies, where uncoupled harmonic oscillators in the same cluster have the identical node dynamics, while any pair of nodes in different clusters are essentially distinguishing according to their local dynamics. A pinning control protocol is proposed for such coupled harmonic oscillators system, and then some graphic topology conditions easy to verify are established for cluster synchronization. The main contributions of the present investigation include: (i) cluster synchronization problem of coupled nonidentical harmonic oscillators is addressed over directed topology; (ii) desynchronizing motion of harmonic oscillators from different clusters doesn't depend on negative coupling weights but leader of every cluster; (iii) this paper deals with what kind of harmonic oscillators ought to be pinned in order to reach cluster synchronization. Finally, numerical examples and simulations demonstrate the obtained theoretical results.     

Sampled-data synchronisation of coupled harmonic oscillators with communication and input delays subject to controller failure

This paper considers the sampled-data synchronisation problems of coupled harmonic oscillators with communication and input delays subject to controller failure. A synchronisation protocol is proposed for such oscillator systems over directed network topology, and then some general algebraic criteria on exponential convergence for the proposed protocol are established. The main features of the present investigation include: (1) both the communication and input delays are simultaneously addressed, and the directed network topology is firstly considered and (2) the effects of time delays on synchronisation performance are theoretically and numerically investigated. It is shown that in the absence of communication delays, coupled harmonic oscillators can achieve synchronisation oscillatory motion. Whereas if communication delays are nonzero at infinite multiple sampled-data instants, its synchronisation (or consensus) state is zero. This conclusion can be used as an effective control strategy to stabilise coupled harmonic oscillators in practical applications. Furthermore, it is interesting to find that increasing either communication or input delays will enhance the synchronisation performance of coupled harmonic oscillators. Subsequently, numerical examples illustrate and visualise theoretical results.     

Synchronization of coupled harmonic oscillators with local interaction

This paper studies synchronization of coupled second-order linear harmonic oscillators with local interaction. We analyze convergence conditions over, respectively, directed fixed and switching network topologies by using tools from algebraic graph theory, matrix theory, and nonsmooth analysis. It is shown that the coupled harmonic oscillators can be synchronized under mild network connectivity conditions. Examples are given to validate the convergence conditions. The theoretical result is also applied to synchronized motion coordination of multi-agent systems as a proof of concept.     

Synchronization of Locally Coupled Neural Oscillators

A new method of controlling Fitzhugh-Nagumo (F-N) neural oscillators, Fitzhugh [1], with local coupling is presented. It is proved that through the use of an additive closed-loop controlling action that entrains each neural oscillator to a goal behavior, necessary and sufficient conditions for the occurrence of synchronization in networks of unidirectionally self-connected neural oscillators are obtained in terms of asymptotic stability. These conditions suggest that rapid global synchronization can be achieved using sufficiently strong local inhibitory connections.     

带有输入和状态时滞的高阶非线性前馈系统的自适应控制

本文考虑了一类高阶不确定非线性前馈系统的自适应镇定问题.将高阶非线性进一步放宽到不仅允许状态时滞,而且还具有未知增长率.通过将自适应方法、动态增益控制方法和增加幂次积分器法结合,设计了一个状态反馈控制器.所设计的控制器保证了闭环系统的所有信号有界,平衡点全局稳定,并且原状态收敛到0.     

时延网络中 Euler-Lagrange 系统的分布式自适应协调控制

对一类含未知参数的Euler-Lagrange系统协调控制问题进行了研究, 提出了一种自适应控制算法. 该算法容许通信网络为最一般的伪强连通图, 并允许通信时延的存在. 对系统中领航者为静态和动态两种情况分别进行了研究, 设计了相应的控制器.研究结果表明,在仅有部分个体能够和领航者进行通信的情况下, 控制器能保证网络中其他个体最终和领航者趋于一致. 运用Lyapunov稳定性定理和Barbalat 定理等对自适应控制器的稳定性进行了证明,并利用数值仿真验证了算法的有效性.     

Exponential Consensus for Nonlinear Multi‐Agent Systems with Communication and Input Delays via Hybrid Control

This paper aims to investigate the exponential leader‐following consensus for nonlinear multi‐agent systems with time‐varying communication and input delays by using hybrid control. Based on the Lyapunov functional method, impulsive differential equation theory and matrix analysis, we show that all the followers can achieve leader‐following consensus with the virtual leader exponentially even if only a fraction of followers can obtain the leader's information. Two classes of exponential consensus criteria as well as the convergence rates for the controlled multi‐agent systems are presented under very relaxed interaction topology conditions, i.e., the directed interaction topology among the followers is only required to have p(p>1) disjoint strong components. Finally, two numerical examples are given to validate the proposed theoretical results.     

含通信延时及输入延时的线性多智能体的一致性

针对通信延时及输入延时并存的情况下,研究具有一般线性动态特性的高阶多智能体在固定且无向的网络拓扑下的一致性.通过将多智能体的特征方程分解为一系列低阶的因子,一致性问题转换为一系列低阶因子的稳定性分析问题,降低了问题的分析复杂度.进一步地,分析无延时情况下多智能体达到一致性的控制增益的取值范围,即增益的稳定区间.当从稳定区间选取一个固定的控制增益时,应用频率扫描高级聚类法分析多个因子在两延时参数空间中的稳定性,并由此获得多智能体延时无关及延时相关的一致性结论.一个说明性的例子验证了分析结论.     

Synchronization of coupled harmonic oscillators in a dynamic proximity network

In this paper, we revisit the synchronization problems for coupled harmonic oscillators in a dynamic proximity network. Unlike many existing algorithms for distributed control of complex dynamical networks that require explicit assumptions on the network connectivity, we show that the coupled harmonic oscillators can always be synchronized, without imposing any network connectivity assumption. Moreover, we also investigate the synchronization with a leader and show that all harmonic oscillators can asymptotically attain the position and velocity of the leader, again without any assumption on connectivity of the followers. Numerical simulation illustrates the theoretical results.     

Pseudo-Predictor Feedback Control for Multiagent Systems with Both State and Input Delays

This paper is concerned with the consensus problem for high-order continuous-time multiagent systems with both state and input delays. A novel approach referred to as pseudo-predictor feedback protocol is proposed. Unlike the predictor-based feedback protocol which utilizes the open-loop dynamics to predict the future states, the pseudo-predictor feedback protocol uses the closed-loop dynamics of the multiagent systems to predict the future agent states. Full-order/reduced-order observer-based pseudo-predictor feedback protocols are proposed, and it is shown that the consensus is achieved and the input delay is compensated by the proposed protocols. Necessary and sufficient conditions guaranteeing the stability of the integral delay systems are provided in terms of the stability of the series of retarded-type time-delay systems. Furthermore, compared with the existing predictor-based protocols, the proposed pseudo-predictor feedback protocol is independent of the input signals of the neighboring agents and is easier to implement. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approaches.      

Cyclic-Pursuit-Based Circular Formation Control of Mobile Agents with Limited Communication Ranges and Communication Delays

This article addresses the circular formation control problem of a multi-agent system moving on a circle in the presence of limited communication ranges and communication delays. To minimize the number of communication links, a novel distributed controller based on a cyclic pursuit strategy is developed in which each agent needs only its leading neighbour’s information. In contrast to existing works, we propose a set of new potential functions to deal with heterogeneous communication ranges and communication delays simultaneously. A new framework based on the admissible upper bound of the formation error is established so that both connectivity maintenance and order preservation can be achieved at the same time. It is shown that the multi-agent system can be driven to the desired circular formation as time goes to infinity under the proposed controller. Finally, the effectiveness of the proposed method is illustrated by some simulation examples.     

变时滞随机忆阻器神经网络的同步控制

在实现实际的复杂人工神经网络模型以及大规模集成电路时,随机噪声是不可避免的.因此,随机忆阻器神经网络具有重要的现实研究意义.针对变时滞随机忆阻器神经网络的同步控制问题,基于非光滑分析以及集值映射、随机微分包含的理论,利用Lyapunov函数和基本不等式的方法,设计了一个线性反馈控制器.通过恰当选择控制器增益,实现了随机忆阻器神经网络驱动系统与相应的响应系统之间的指数同步,所得到的结果保守性更小.最后,给出数值例子验证了理论结果的有效性.     

脉冲同步在数字保密通信中的应用

首先给出了蔡氏混沌电路的脉冲同步方法，同时给出了其同步的渐进稳定条件，最后构造了一个基于脉冲同步的数字保密通信系统，系统实验表明应用脉冲同步具有高保密性和鲁棒性。     

Synchronization for an array of coupled stochastic discrete-time neural networks with mixed delays

In this paper, a synchronization problem is investigated for an array of coupled stochastic discrete-time neural networks with both discrete and distributed time-varying delays. By utilizing a novel Lyapunov function and the Kronecker product, it is shown that the addressed stochastic discrete-time neural networks is synchronized if certain linear matrix inequalities (LMIs) are feasible. Neither any model transformation nor free-weighting matrices are employed in the derivation of the results obtained, and they can be solved efficiently via the Matlab LMI Toolbox. The proposed synchronization criteria are less conservative than some recently known ones in the literature, which is demonstrated via two numerical examples.     

耦合调和振子网络系统的联合连通同步

论文分析了耦合调和振子网络系统在联合连通网络拓扑结构下的引导-跟随同步问题.假定每个网络拓扑结构图不连通,但它们在有限时间内能够联合连通,利用代数图论,李雅普诺夫稳定性理论和La Salle不变原理,证明了该系统的同步稳定性.最后,数值模拟进一步验证了所得理论结果的正确性和有效性.     

Synchronization analysis of coupled connected neural networks with mixed time delays

In this paper, the global exponential synchronization of coupled connected neural networks with both discrete and distributed delays is investigated under mild condition, assuming neither the differentiability and strict monotonicity for the activation functions nor the diagonal for the inner coupling matrices. By employing a new Lyapunov–Krasovskii functional, applying the theory of Kronecker product of matrices and the linear matrix inequality (LMI) technique, several delay-dependent sufficient conditions in LMI form are obtained for global exponential synchronization of such systems. Moreover, the decay rate is estimated. The proposed LMI approach has the advantage of considering the difference of neuronal excitatory and inhibitory efforts, which is also computationally efficient as it can be solved numerically using efficient Matlab LMI toolbox, and no tuning of parameters is required. In addition, the proposed results generalize and improve the earlier publications. An example with simulation is given to show the effectiveness of the obtained results.     

Consensus of Multi-Agent Systems With Diverse Input and Communication Delays

The consensus problem for multi-agent systems with input and communication delays is studied based on the frequency-domain analysis. Two decentralized consensus conditions are obtained, one of which is given for the systems based on undirected graphs with diverse input delays and the other is for the systems based on directed graphs with diverse communication delays and input delays. For the systems with both communication delays and input delays, the consensus condition is dependent on input delays but independent of communication delays.     

参数未知的自适应耦合同步及其在保密通信中的应用

在实际应用中,系统参数会随着环境的变化而变化,因此研究参数不确定混沌系统的同步更具有实际应用价值。文章针对参数完全未知的混沌系统,基于单向耦合同步方法,实现了混沌系统的自适应同步,为证明系统同步进行了严格的数学推导,并将同步的混沌系统应用到混沌保密通信中。计算机仿真表明混沌系统能够快速达到同步,且在混沌保密通信系统的接收端,有用信号可以有效地恢复出来,从而证明文章提出的方法有效且可行。     

矿井透地通信系统中的定时同步研究

对矿井透地通信系统中的定时同步问题进行了研究。首先以大地信道为对象构建了简单的弹性波介质模型,计算得到该模型的多径延时为20 ms;其次在Matlab环境中仿真并对比分析了非数据辅助定时定时同步方法和数据辅助定时同步方法在透地通信系统定时同步应用中的性能,得出非数据辅助定时同步方法对透地通信系统的信号功率要求较高、数据辅助定时同步方法具有较高可靠性且更适合透地通信系统的结论;最后对采用数据辅助定时同步方法,当OFDM信号的循环前缀长度分别为最大时延的0.5倍、2倍、4倍,信噪比为0~18 dB的透地通信系统解码误码率进行了仿真研究,结果表明,当OFDM信号的循环前缀长度大于最大时延的2倍、信噪比大于16 dB时,透地通信系统的解码误码率可达10-5数量级,从而验证了数据辅助定时同步方法应用于透地通信系统同步解码时的可靠性。     

Synchronization of Complex Networks with Coupled and Self‐Feedback Delays Via Aperiodically Intermittent Strategy

In this paper, we concern the exponential synchronization problem for hybrid‐coupled delayed dynamical networks via aperiodically intermittent control. Different from previous works, the delayed coupling term considered here contains the transmission delay and self‐feedback delay, and the intermittent control can be aperiodic. By utilizing a different technique compared with some previous results, several useful criteria are derived analytically to realise exponential synchronization for a class of coupled complex network. As a special case, some sufficient conditions ensuring the exponential synchronization for a class of coupled neural network are obtained. Finally, a numerical example is given to demonstrate the validness of the proposed scheme.