Synchronization of linear dynamical networks on time scales: Pinning control via delayed impulses
Synchronization of linear dynamical networks on time scales: Pinning control via delayed impulses
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DOI：
10.1016/j.automatica.2016.06.001
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发表时间：
2016-10
期刊：
影响因子：
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通讯作者：
Xinzhi Liu;Kexue Zhang
中科院分区：
文献类型：
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作者：
Xinzhi Liu;Kexue Zhang
研究了复杂动态网络在时间尺度上的同步问题。设计了一种考虑时延影响的钉扎脉冲控制方案，实现了CDN在时间尺度上与孤立节点状态的同步。基于时间尺度理论和直接Lyapunov方法，建立了一般时间尺度上线性CDN的同步准则。我们的结果表明，通过脉冲控制一小部分节点，可以在时间尺度上达成CDN的共识。根据我们的钉扎脉冲控制方案，在每个脉冲时刻选择不同数目的节点，并且在钉扎脉冲中考虑时延。本文提出的建模框架是对已有的连续时间和离散时间CDN模型的统一和推广，而钉扎脉冲控制方案则是对已有的连续时间CDN同步控制方案的扩展。此外，在时间尺度上研究动态系统的思想为同时研究连续时间系统及其离散时间系统提供了一种统一的方法。数值仿真结果验证了理论分析的有效性。
This paper studies the synchronization problem of complex dynamical networks (CDNs) on time scales. A pinning impulsive control scheme that takes into account of time-delay effects is designed to achieve synchronization of CDNs on time scales with the state of an isolated node. Based on the theory of time scales and the direct Lyapunov method, a synchronization criterion is established for linear CDNs on general time scales. Our result shows that, by impulsive control a small portion of nodes, the consensus of CDNs on time scales can be achieved. According to our pinning impulsive control scheme, different numbers of nodes will be selected at each impulsive instant and time delay is considered in the pinning impulses. The modeling framework developed in this paper is a unification and generalization of many existing continuous-time and discrete-time CDN models, while the pinning impulsive control scheme is an extension of the existing control scheme for synchronization of continuous-time CDNs. Moreover, the idea of studying dynamical systems on time scales provide a unified approach to investigate continuous-time system and its discrete-time counterpart simultaneously. Numerical simulations are given to illustrate the effectiveness of the theoretical analysis.