Identification algorithm of switched systems based on generalized auxiliary model

doi:10.21629/JSEE.2019.06.16

Abstract

Abstract:

For switched linear system with colored measurement noises, the identification difficulties of this system are that there exist unknown switching information, unknown middle variables and noise terms in the information vector. For the mentioned issues, the fuzzy clustering and the multi-innovation recursive identification algorithm are used to deal with these problems. Firstly, the mode detection is transformed into the detection of membership degree values confirmed by the fuzzy clustering method, and the problem of mode detection is solved by judgment and decision of the fuzzy membership values. Moreover, the multi-innovation recursive identification algorithm based on the generalized auxiliary model is proposed to estimate the parameters of the switched linear system with colored noises. Finally, the effectiveness of the proposed method is verified by the results of the simulation example.

CLC Number:

Hongwei WANG, Hao XIA. Identification algorithm of switched systems based on generalized auxiliary model[J]. Journal of Systems Engineering and Electronics, 2019, 30(6): 1224-1232.

Figures/Tables 10

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Information length	$p=1$	$p=3$	$p=5$
GRFD	[71.5%, 86.6%]	[75.5%, 89.6%]	[84.5%, 98.6%]
AV	80.8%	83.8%	94.7%

Model	The algorithm in [15]	Our algorithm $(p=5)$
Model 1	$\widehat {\mathit{\boldsymbol{\theta}} }_1 =\left[\!\!\begin{array}{*{20}c} { - 0.398\pm 0.019} \\ {0.251\pm 0.024} \\ { - 0.148\pm 0.052} \\ {0.081\pm 0.015} \end{array}\!\!\right]$	$\widehat {\mathit{\boldsymbol{\theta}} }_1 = \left[\!\!\begin{array}{*{20}c} { - 0.400~1\pm 0.003} \\ {0.249~8\pm 0.002}\\ { - 0.148~7\pm 0.001} \\ {0.080~1\pm 0.003} \end{array}\!\!\right]$
Real parameter: $\mathit{\boldsymbol{\theta}} _1 = [-0.4, 0.25, -0.15, 0.08]^{\rm T} $
Model 2	$\widehat {\mathit{\boldsymbol{\theta}} }_2 =\left[\!\!\begin{array}{*{20}c} {0.983\pm 0.037~8} \\ {0.235~5\pm 0.024~6} \\{ - 0.649\pm 0.037~1}\\{0.298~7\pm 0.041~5} \end{array}\!\!\right]$	$\widehat {\mathit{\boldsymbol{\theta}} }_2 = \left[\!\!\begin{array}{*{20}c} {0.999~6\pm 0.002}\\ {0.239~4\pm 0.003} \\{ - 0.650~4\pm 0.003}\\ {0.299~8\pm 0.004} \end{array}\!\!\right]$
Real parameter: $\mathit{\boldsymbol{\theta}} _2 = [1, 0.24, -0.65, 0.3]^{\rm T} $
Model 3	$\widehat {\mathit{\boldsymbol{\theta}} }_3 =\left[\!\!\begin{array}{*{20}c} {1.557~7\pm 0.025}\\ { - 0.571~6\pm 0.038}\\ { - 2.076~8\pm 0.071} \\ {0.964~5\pm 0.044~9} \end{array}\!\!\right]$	$\widehat {\mathit{\boldsymbol{\theta}} }_3 = \left[\!\!\begin{array}{*{20}c} {1.550~5\pm 0.001~2} \\ { - 0.579\pm 0.002~6} \\ { - 2.101\pm 0.004~2} \\{0.959~6\pm 0.003~0} \end{array}\!\!\right]$
Real parameter: $\mathit{\boldsymbol{\theta}} _3 =[1.55, -0.58, -2.1, 0.96]^{\rm T} $
Noise model	$\mathit{\boldsymbol{D}} = \left[\!\!\begin{array}{*{20}c} { - 0.949\pm 0.09} \\ {0.159\pm 0.04} \end{array}\!\!\right]$	$\mathit{\boldsymbol{D}} = \left[\!\!\begin{array}{*{20}c} { - 0.985~5\pm 0.015} \\ {0.192~6\pm 0.012} \end{array}\!\!\right]$
Real parameter: $\mathit{\boldsymbol{D}} =[-1, 0.2]^{\rm T} $