Quantised polynomial filtering for nonlinear systems with missing measurements

This paper is concerned with the polynomial filtering problem for a class of nonlinear systems with quantisations and missing measurements. The nonlinear functions are approximated with polynomials of a chosen degree and the approximation errors are described as low-order polynomial terms with norm-...

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Published in:International journal of control Vol. 91; no. 10; pp. 2250 - 2260
Main Authors: Liu, Yang, Wang, Zidong, Zhou, D. H.
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 03.10.2018
Taylor & Francis Ltd
Subjects:
Algorithms
Approximation
Covariance
Filter design (mathematics)
Filtration
Functions (mathematics)
Mathematical analysis
missing measurements
Nonlinear filtering
Nonlinear systems
polynomial approximation
Polynomials
quantisation
recursive algorithm
Upper bounds
ISSN:0020-7179, 1366-5820
Online Access:Get full text
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Abstract This paper is concerned with the polynomial filtering problem for a class of nonlinear systems with quantisations and missing measurements. The nonlinear functions are approximated with polynomials of a chosen degree and the approximation errors are described as low-order polynomial terms with norm-bounded coefficients. The transmitted outputs are quantised by a logarithmic quantiser and are also subject to randomly missing measurements governed by a Bernoulli distributed sequence taking values on 0 or 1. Dedicated efforts are made to derive an upper bound of the filtering error covariance in the simultaneous presence of the polynomial approximation errors, the quantisations as well as the missing measurements at each time instant. Such an upper bound is then minimised through designing a suitable filter gain by solving a set of matrix equations. The filter design algorithm is recursive and therefore applicable for online computation. An illustrative example is exploited to show the effectiveness of the proposed algorithm.
AbstractList This paper is concerned with the polynomial filtering problem for a class of nonlinear systems with quantisations and missing measurements. The nonlinear functions are approximated with polynomials of a chosen degree and the approximation errors are described as low-order polynomial terms with norm-bounded coefficients. The transmitted outputs are quantised by a logarithmic quantiser and are also subject to randomly missing measurements governed by a Bernoulli distributed sequence taking values on 0 or 1. Dedicated efforts are made to derive an upper bound of the filtering error covariance in the simultaneous presence of the polynomial approximation errors, the quantisations as well as the missing measurements at each time instant. Such an upper bound is then minimised through designing a suitable filter gain by solving a set of matrix equations. The filter design algorithm is recursive and therefore applicable for online computation. An illustrative example is exploited to show the effectiveness of the proposed algorithm.
Author Liu, Yang
Wang, Zidong
Zhou, D. H.
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  surname: Zhou
  fullname: Zhou, D. H.
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  organization: Department of Automation, Tsinghua University
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Cites_doi 10.1137/S0363012993252899
10.1142/1347
10.1109/TFUZZ.2015.2446509
10.1016/j.automatica.2015.11.008
10.1109/TCYB.2014.2356560
10.1103/PhysRevD.93.122007
10.1109/TAC.2009.2037467
10.1016/j.neucom.2016.06.046
10.1109/TAC.2013.2241492
10.1134/S0005117916010033
10.1109/TCST.2016.2557221
10.1080/00207721.2014.919713
10.1109/CDC.2003.1272678
10.1109/TAC.2004.834121
10.1109/9.618240
10.1109/TAC.2015.2437526
10.1109/TAC.2007.908347
10.1016/j.sigpro.2011.09.026
10.1016/j.apm.2008.12.008
10.1007/s10514-015-9530-4
10.1016/j.automatica.2015.02.022
10.1016/j.automatica.2016.01.019
10.1016/j.sigpro.2016.02.014
10.1016/j.inffus.2016.06.008
10.1016/j.automatica.2012.03.027
10.1016/j.automatica.2015.02.024
10.1109/TAC.2005.860256
10.1049/iet-cta.2015.0849
10.1109/TAC.2010.2041611
10.1002/acs.1074
10.1002/rnc.1441
10.4173/mic.2009.1.3
10.1016/j.neucom.2016.01.058
10.1080/00207721.2013.807387
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cit0033
cit0012
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cit0017
cit0018
cit0015
cit0037
cit0016
cit0038
cit0013
cit0035
cit0014
cit0022
cit0001
cit0023
cit0021
Zhong M. (cit0039) 2015; 15
Bellman R (cit0005) 1970
Hu L. (cit0020) 2012; 24
Basin M (cit0002) 2008
cit0008
Wu Y. (cit0036) 2015; 353
cit0009
cit0006
cit0028
cit0007
cit0029
cit0004
cit0026
cit0027
cit0024
cit0003
cit0025
References_xml – ident: cit0009
  doi: 10.1137/S0363012993252899
– ident: cit0023
  doi: 10.1142/1347
– ident: cit0037
  doi: 10.1109/TFUZZ.2015.2446509
– ident: cit0019
  doi: 10.1016/j.automatica.2015.11.008
– ident: cit0008
  doi: 10.1109/TCYB.2014.2356560
– ident: cit0001
  doi: 10.1103/PhysRevD.93.122007
– ident: cit0022
  doi: 10.1109/TAC.2009.2037467
– ident: cit0031
  doi: 10.1016/j.neucom.2016.06.046
– ident: cit0032
  doi: 10.1109/TAC.2013.2241492
– ident: cit0025
  doi: 10.1134/S0005117916010033
– ident: cit0033
  doi: 10.1109/TCST.2016.2557221
– ident: cit0038
  doi: 10.1080/00207721.2014.919713
– ident: cit0013
  doi: 10.1109/CDC.2003.1272678
– ident: cit0029
  doi: 10.1109/TAC.2004.834121
– ident: cit0010
  doi: 10.1109/9.618240
– ident: cit0012
  doi: 10.1109/TAC.2015.2437526
– ident: cit0015
  doi: 10.1109/TAC.2007.908347
– ident: cit0003
  doi: 10.1016/j.sigpro.2011.09.026
– ident: cit0017
  doi: 10.1016/j.apm.2008.12.008
– volume: 24
  start-page: 703
  issue: 2
  year: 2012
  ident: cit0020
  publication-title: IEEE Transactions on Control Systems Technology,
– ident: cit0030
  doi: 10.1007/s10514-015-9530-4
– volume-title: Introduction to matrix analysis
  year: 1970
  ident: cit0005
– ident: cit0024
  doi: 10.1016/j.automatica.2015.02.022
– ident: cit0028
  doi: 10.1016/j.automatica.2016.01.019
– volume: 15
  start-page: 2785
  issue: 5
  year: 2015
  ident: cit0039
  publication-title: IEEE Sensors Journal,
– volume-title: New trends in optimal filtering and control for polynomial and time-delay systems
  year: 2008
  ident: cit0002
– ident: cit0006
  doi: 10.1016/j.sigpro.2016.02.014
– ident: cit0007
  doi: 10.1016/j.inffus.2016.06.008
– ident: cit0018
  doi: 10.1016/j.automatica.2012.03.027
– ident: cit0011
  doi: 10.1016/j.automatica.2015.02.024
– ident: cit0014
  doi: 10.1109/TAC.2005.860256
– ident: cit0027
  doi: 10.1049/iet-cta.2015.0849
– ident: cit0026
  doi: 10.1109/TAC.2010.2041611
– volume: 353
  start-page: 144
  issue: 1
  year: 2015
  ident: cit0036
  publication-title: Journal of the Franklin Institute-Engineering and Applied Mathematics,
– ident: cit0004
  doi: 10.1002/acs.1074
– ident: cit0016
  doi: 10.1002/rnc.1441
– ident: cit0021
  doi: 10.4173/mic.2009.1.3
– ident: cit0034
  doi: 10.1016/j.neucom.2016.01.058
– ident: cit0035
  doi: 10.1080/00207721.2013.807387
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SubjectTerms Algorithms
Approximation
Covariance
Filter design (mathematics)
Filtration
Functions (mathematics)
Mathematical analysis
missing measurements
Nonlinear filtering
Nonlinear systems
polynomial approximation
Polynomials
quantisation
recursive algorithm
Upper bounds
Title Quantised polynomial filtering for nonlinear systems with missing measurements
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