Finite-time Synchronization Between Uncertain Complex Networks Based on Unidirectional Coupling Method
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摘要:
针对具有不确定性的复杂网络有限时间同步问题, 提出一种新颖的单向耦合控制方法. 构建含有未知参量及未知拓扑结构的驱动−响应复杂网络模型, 考虑两个网络具有不同的节点数, 同时受到时变耦合时滞的影响, 并且网络内部分别具有不同的节点系统. 基于有限时间稳定性理论和线性矩阵不等式变换, 通过在响应网络中引入单向耦合项, 实现两个网络间的有限时间同步, 同时准确辨识未知参量及未知拓扑结构. 仿真实验验证所提同步方法的有效性, 对比实验结果表明所提方法在减少耦合数量的同时具有更快的同步速率及更小的波动范围.
Abstract:To solve the problem of finite-time synchronization of uncertain complex networks, a novel unidirectional coupling control method is proposed. First, a drive-response complex network model with unknown parameters and unknown topological structure is constructed. The two networks have different sizes, and each of which contains two types of nonidentical nodes and time-varying coupling delay. Based on the finite-time stability theory and the linear matrix inequality, the finite-time synchronization between two networks is realized by adding a unidirectional coupling term in the response network, the unknown parameters and the unknown topological structure can be identified, simultaneously. The simulation experiments verify the validity of the proposed scheme. Moreover, the comparison experiments show that the proposed method achieves faster synchronization rate and smaller fluctuation range as well as reduced coupling quantity.
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图 1 同步误差的演化
${e_{i1}}(t),{e_{i2}}(t),{e_{i3}}(t)\ (i = 1,2, \cdots ,10)$ Fig. 1 Synchronous errors
${e_{i1}}(t),\;{e_{i2}}(t),\;{e_{i3}}(t)\left(i = 1,2, \cdots ,10\right)$ 
图 2 未知参量的辨识
${\hat a_{1i}}\left( {i = 1,2, \cdots ,5} \right)$ Fig. 2 Identification of the unknown parameters
${\hat a_{1i}}\left( {i = 1,2, \cdots ,5} \right)$ 
图 3 未知参量的辨识
${\hat d_{2i}}\left( {i = 6,7, \cdots ,10} \right)$ Fig. 3 Identification of the unknown parameters
${\hat d_{2i}}\left( {i = 6,7, \cdots ,10} \right)$ 
图 4 未知拓扑结构的辨识
${\hat{c}_{ij}}$ Fig. 4 Identification of network structure
${\hat{c}_{ij}}$ 
图 5 未知拓扑结构的辨识
${\hat{c}_{ij}}$ Fig. 5 Identification of network structure
${\hat{c}_{ij}}$ 
图 6 未知拓扑结构的辨识
${\hat{c}_{ij}}$ Fig. 6 Identification of network structure
${\hat{c}_{ij}}$ 
图 7 未知拓扑结构的辨识
${\hat{c}_{ij}}$ Fig. 7 Identification of network structure
${\hat{c}_{ij}}$ -
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