基于時(shí)滯測量的復雜網(wǎng)絡(luò )分布式狀態(tài)估計研究
doi: 10.16383/j.aas.c210921
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廣東工業(yè)大學(xué)自動(dòng)化學(xué)院廣東省智能決策與協(xié)同控制重點(diǎn)實(shí)驗室 廣州 510006
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北京航空航天大學(xué)杭州創(chuàng )新研究院(余杭) 杭州 310023
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北京航空航天大學(xué)儀器科學(xué)與光電工程學(xué)院 北京 100191
Distributed State Estimation for Complex Networks With Delayed Measurements
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Guangdong Provincial Key Laboratory of Intelligent Decision and Cooperative Control, School of Automation, Guangdong University of Technology, Guangzhou 510006
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Hangzhou Innovation Institute (Yuhang), Beihang University, Hangzhou 310023
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School of Instrumentation and Optoelectronic Engineering, Beihang University, Beijing 100191
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摘要: 研究一類(lèi)存在一步隨機時(shí)滯的復雜網(wǎng)絡(luò )分布式狀態(tài)估計問(wèn)題, 采用伯努利隨機變量刻畫(huà)測量值的隨機時(shí)滯情況. 基于復雜網(wǎng)絡(luò )模型和不可靠測量值, 分別設計復雜網(wǎng)絡(luò )的狀態(tài)預測器和分布式狀態(tài)估計器, 基于楊氏不等式消除節點(diǎn)之間的耦合項, 通過(guò)優(yōu)化楊氏不等式引進(jìn)的參數, 優(yōu)化狀態(tài)預測協(xié)方差. 通過(guò)設計估計器增益, 獲得狀態(tài)估計誤差協(xié)方差, 同時(shí)結合預測誤差協(xié)方差, 獲得狀態(tài)估計誤差協(xié)方差的迭代公式, 并給出估計誤差協(xié)方差穩定的充分條件. 最后, 對由小車(chē)組成的耦合系統進(jìn)行數值仿真, 驗證所設計估計器的有效性.
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關(guān)鍵詞:
- 復雜網(wǎng)絡(luò ) /
- 分布式狀態(tài)估計 /
- 時(shí)滯測量 /
- 穩定性分析
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.-
Key words:
- Complex network /
- distributed state estimation /
- delayed measurement /
- stability analysis
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圖 3 優(yōu)化和未優(yōu)化的$ \gamma_{1,i,k} $
Fig. 3 $ \gamma_{1,i,k} $ with and without optimization
圖 4 基于優(yōu)化和未優(yōu)化$ \gamma_{1,1,k} $的第1個(gè)節點(diǎn)的估計誤差協(xié)方差上界的跡和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
圖 5 基于優(yōu)化和未優(yōu)化$ \gamma_{1,2,k} $的第2個(gè)節點(diǎn)的估計誤差協(xié)方差上界的跡和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
圖 6 基于優(yōu)化和未優(yōu)化$ \gamma_{1,3,k} $的第3個(gè)節點(diǎn)的估計誤差協(xié)方差上界的跡和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
圖 7 基于優(yōu)化和未優(yōu)化$ \gamma_{1,4,k} $的第4個(gè)節點(diǎn)的估計誤差協(xié)方差上界的跡和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 基于優(yōu)化和未優(yōu)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
節點(diǎn)$i$ 未優(yōu)化$\rm{tr}(P_{i,k|k})$上界 優(yōu)化后$\rm{tr}(P_{i,k|k})$上界 優(yōu)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 基于優(yōu)化和未優(yōu)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
節點(diǎn)$i$ 未優(yōu)化MSE$_{i,k|k}$均值 優(yōu)化后MSE$_{i,k|k}$均值 優(yōu)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
下載: 導出CSV
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