Exponential Synchronization of Discrete Uncertain Spatiotemporal Networks With Topology Switching Characteristics
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摘要: 研究了具有拓扑切换特性的离散型不确定时空网络的指数同步问题. 基于稳定性理论, 构造了具有指数形式的Lyapunov函数, 并设计了同步控制器的结构方程, 进而获得了时空网络的同步条件. 同时, 我们设计了未知参数的识别律, 有效地识别了网络中的未知参数. 最后, 选取实际的激光相位共轭波空间扩展系统作为网络节点进行仿真模拟, 验证了同步方案的可行性与控制器的有效性. 通过构造具有指数形式的Lyapunov函数, 能够有效地调节网络的同步速率. 并且获得的同步条件中不包含网络的耦合矩阵项, 消除了拓扑切换特性对同步过程的影响, 使得网络同步性能更加稳定.Abstract: The exponential synchronization problem of discrete uncertain spatiotemporal networks with topology switching characteristics is researched. Based on the stability theory, the Lyapunov function with exponential form is constructed and the structural equation of the synchronous controller is designed, and then the synchronization condition of the spatiotemporal network is obtained. Meanwhile, the unknown parameters of the network are identifled efiectively by designing the identiflcation law of the unknown parameters. Finally, we use phase-conjugate wave spatial expanded system as the nodes of the network to simulate, and the feasibility of the synchronization scheme and the efiectiveness of the controller is verifled. By constructing the Lyapunov function with exponential form, the synchronization rate of the network can be adjusted efiectively. In addition, the synchronization condition does not contain the coupling matrix term of the network, which eliminates the influence of the topology switching characteristics on the synchronization process, and makes the network synchronization performance more stable.
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Key words:
- Topology switching /
- discrete spatiotemporal networks /
- parameter identiflcation /
- exponential synchronization
1) 本文责任编委 张卫东 -
图 11 未知参数$\varepsilon_1(m, n)$随时空的演化
Fig. 11 Spatiotemporal evolution of unknown parameter $\varepsilon_1(m, n)$
图 12 未知参数$\varepsilon_2(m, n)$随时空的演化
Fig. 12 Spatiotemporal evolution of unknown parameter $\varepsilon_2(m, n)$
图 13 未知参数$\varepsilon_3\, (m, n)$随时空的演化
Fig. 13 Spatiotemporal evolution of unknown parameter $\varepsilon_3\, (m, n)$
图 14 未知参数$\varepsilon_4(m, n)$随时空的演化
Fig. 14 Spatiotemporal evolution of unknown parameter $\varepsilon_4(m, n)$
图 15 未知参数$\varepsilon_5(m, n)$随时空的演化
Fig. 15 Spatiotemporal evolution of unknown parameter $\varepsilon_5(m, n)$
图 16 未知参数$\varepsilon_6(m, n)$随时空的演化
Fig. 16 Spatiotemporal evolution of unknown parameter $\varepsilon_6(m, n)$
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