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摘要: 研究一类存在一步随机时滞的复杂网络分布式状态估计问题, 采用伯努利随机变量刻画测量值的随机时滞情况. 基于复杂网络模型和不可靠测量值, 分别设计复杂网络的状态预测器和分布式状态估计器, 基于杨氏不等式消除节点之间的耦合项, 通过优化杨氏不等式引进的参数, 优化状态预测协方差. 通过设计估计器增益, 获得状态估计误差协方差, 同时结合预测误差协方差, 获得状态估计误差协方差的迭代公式, 并给出估计误差协方差稳定的充分条件. 最后, 对由小车组成的耦合系统进行数值仿真, 验证所设计估计器的有效性.Abstract: This work addresses the distributed state estimation for complex networks with delayed measurements. The Bernoulli process is employed to describe the measurements with randomly occurred one step delay. The state predictor is derived based on the system mode, and the distributed state estimator is designed by using delayed measurements. The coupling term between nodes is eliminated based on Young＇s inequality, and the covariance of state prediction is improved by optimizing the parameters introduced by Young＇s inequality. Furthermore, the optimal state estimation error covariance is achieved by designing the estimator gain. Thanks to the state prediction error covariance, the iterative inequality of the state estimation error covariance is derived, and its sufficient condition for stability is established. Finally, the moving vehicles based coupled system is given to illustrate the effectiveness of the designed estimator.
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Key words:
- Complex network /
- distributed state estimation /
- delayed measurement /
- stability analysis
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图 4 基于优化和未优化$ \gamma_{1,1,k} $的第1个节点的估计误差协方差上界的迹和MSE
Fig. 4 The trace of upper bound of the estimation error covariance and the MSE of the node 1 based on $ \gamma_{1,1,k} $ with and without optimization
图 5 基于优化和未优化$ \gamma_{1,2,k} $的第2个节点的估计误差协方差上界的迹和MSE
Fig. 5 The trace of upper bound of the estimation error covariance and the MSE of the node 2 based on $ \gamma_{1,2,k} $ with and without optimization
图 6 基于优化和未优化$ \gamma_{1,3,k} $的第3个节点的估计误差协方差上界的迹和MSE
Fig. 6 The trace of upper bound of the estimation error covariance and the MSE of the node 3 based on $ \gamma_{1,3,k} $ with and without optimization
图 7 基于优化和未优化$ \gamma_{1,4,k} $的第4个节点的估计误差协方差上界的迹和MSE
Fig. 7 The trace of upper bound of the estimation error covariance and the MSE of the node 4 based on $ \gamma_{1,4,k} $ with and without optimization
表 1 基于优化和未优化的$\gamma_{1,i,k}$的上界$\rm{tr}(P_{i,k|k})$
Table 1 The upper bound $\rm{tr}(P_{i,k|k})$ based on $\gamma_{1,i,k}$ with and without optimization
节点$i$ 未优化$\rm{tr}(P_{i,k|k})$上界 优化后$\rm{tr}(P_{i,k|k})$上界 优化幅度(%) 1 0.0679 0.0622 8.50 2 0.0686 0.0630 8.23 3 0.0806 0.0733 9.04 4 0.0768 0.0717 6.60 
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表 2 基于优化和未优化的$\gamma_{1,i,k}$的MSE$_{i,k|k}$
Table 2 The MSE$_{i,k|k}$ based on $\gamma_{1,i,k}$ with and without optimization
节点$i$ 未优化MSE$_{i,k|k}$均值 优化后MSE$_{i,k|k}$均值 优化幅度(%) 1 0.0357 0.0338 5.23 2 0.0364 0.0347 4.82 3 0.0424 0.0400 5.73 4 0.0456 0.0438 3.83
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