Subspace Clustering on Parameter Estimation of Switched Affine Models
详细信息 查看官网全文
- 英文论文题名：Subspace Clustering on Parameter Estimation of Switched Affine Models
- 论文作者：Liang Li ; Jiannan Liu
- 英文论文作者：Liang Li ; Jiannan Liu ; The No.719 Research Institute of CSIC ; National Lab of Science and Technology on Steam Power for NS
- 年：2017
- 作者机构：The No.719 Research Institute of CSIC;National Lab of Science and Technology on Steam Power for NS;
- 英文论文关键词：System identification ; Parameter estimation ; Switched affine systems ; Subspace estimation ; Spectral clustering
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（B）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（B）
- 语种：英文
- 分类号：O212.1
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：6
- 文件大小：253k
- 原文格式：D
- 会议级别：全国
摘要
The problem of estimating parameters of switched affine systems with noisy input-output observations is considered.A subspace technique is proposed to exploit the observations' permutation structure, which transforms the problem of associating observations with subsystems into one of de-permutating a block diagonal matrix. Then a spectral clustering algorithm is presented to recover the block structure of observations, from which each observation is related to a particular subsystem. With the labelled observations, parameters of the submodel are estimated via the total least squares(TLS) estimator. The proposed technique is applicable to switched affine systems with arbitrarily shaped domain partitions, and it offers significantly improved performance and lowered computation complexity than existing techniques.
The problem of estimating parameters of switched affine systems with noisy input-output observations is considered.A subspace technique is proposed to exploit the observations' permutation structure, which transforms the problem of associating observations with subsystems into one of de-permutating a block diagonal matrix. Then a spectral clustering algorithm is presented to recover the block structure of observations, from which each observation is related to a particular subsystem. With the labelled observations, parameters of the submodel are estimated via the total least squares(TLS) estimator. The proposed technique is applicable to switched affine systems with arbitrarily shaped domain partitions, and it offers significantly improved performance and lowered computation complexity than existing techniques.
The problem of estimating parameters of switched affine systems with noisy input-output observations is considered.A subspace technique is proposed to exploit the observations' permutation structure, which transforms the problem of associating observations with subsystems into one of de-permutating a block diagonal matrix. Then a spectral clustering algorithm is presented to recover the block structure of observations, from which each observation is related to a particular subsystem. With the labelled observations, parameters of the submodel are estimated via the total least squares(TLS) estimator. The proposed technique is applicable to switched affine systems with arbitrarily shaped domain partitions, and it offers significantly improved performance and lowered computation complexity than existing techniques.
引文
[1]W.Heemels,B.D.Schutter,and A.Bemporad,“Equivalence of hybrid dynamic models,”Automatica,vol.37,no.7,2001.
[2]Y.D.Ji and H.J.Chizeck,“Controllability,stabilizability,and continuous-time markovian jump linear quadratic control,”IEEE Transactions on Automatic Control,vol.35,no.7,pp.777-788,1990.
[3]P.Grieder,M.Kvasnica,M.Baotic,and M.Morati,“Stabilizing low complexity feedback control of constrained piecewise affine systems,”Automatica,vol.41,no.10,pp.1683-1694,2005.
[4]L.Habets,P.J.Collins,and J.H.van Schuppen,“Reachability and control synthesis for piecewise-affine hybrid systems on simplices,”IEEE Transactions On Automatic Control,vol.51,no.6,pp.938-948,2006.
[5]M.Zhong,H.Ye,P.Shi,and G.Wang,“Fault detection for markovian jump systems,”IEE Proceedings Control Theory and Applications,vol.152,no.4,pp.397-402,2005.
[6]N.Meskin and K.Khorasani,“A geometric approach to fault detection and isolation of continuous-time markovian jump linear systems,”IEEE Transactions on Automatic Control,vol.55,no.6,pp.1343-1357,2010.
[7]L.G.Wu,X.M.Yao,and W.X.Zheng,“Generalized h-2 fault detection for two-dimensional markovian jump systems,”Automatica,vol.48,no.8,pp.1741-1750,2012.
[8]A.Guha and A.Biswas,“An overview of modeling techniques for hybrid brain data,”Statistica Sinica,vol.18,no.4,pp.1311-1340,2008.
[9]R.Vidal,M.Yi,and S.Sastry,“Generalized principal component analysis(gpca),”IEEE Transactions on Pattern Analysis and Machine Intelligence,vol.27,no.12,pp.1945-1959,2005.
[10]P.Turaga,R.Chellappa,V.S.Subrahmanian,and O.Udrea,“Machine recognition of human activities:A survey,”IEEETransactions On Circuits And Systems For Video Technology,vol.18,no.11,pp.1473-1488,2008.
[11]R.Vidal,“Subspace clustering,”IEEE Signal Processing Magazine,vol.28,no.2,pp.52-68,2011.
[12]A.Doucet,A.Logothetis,and V.Krishnamurthy,“Stochastic sampling algorithms for state estimation of jump markov linear systems,”IEEE Transactions on Automatic Control,vol.45,no.2,pp.188-202,2000.
[13]C.Biao and T.Lang,“Traffic-aided multiuser detection for random-access cdma networks,”IEEE Transactions on Signal Processing,vol.49,no.7,pp.1570-1580,2001.
[14]A.Juloski,W.Heemels,G.Ferrari-Trecate,R.Vidal,S.Paoletti,and J.Niessen,“Comparison of four procedures for the identification of hybrid systems,”in Hybrid systems:computation and control:8th international workshop(HSCC’2005),Zurich,Switzerland,2005,pp.354-369.
[15]S.Paoletti,A.L.Juloski,G.Ferrari-Trecate,and R.Vidal,“I-dentification of hybrid systems-a tutorial,”European Journal Of Control,vol.13,no.2-3,pp.242-260,2007.
[16]G.Ferrari-Trecate,M.Muselli,D.Liberati,and M.Morari,“Aclustering technique for the identification of piecewise affine systems,”Automatica,vol.39,no.2,2003.
[17]M.E.Gegundez,J.Aroba,and J.M.Bravo,“Identification of piecewise affine systems by means of fuzzy clustering and competitive learning,”Engineering Applications Of Artificial Intelligence,vol.21,no.8,pp.1321-1329,2008.
[18]L.Li,W.Dong,Y.D.Ji,and Z.K.Zhang,“An improved parameter identification approach for piecewise affine model,”Control Engineering Practice,vol.21,no.1,pp.54-64,2013.
[19]T.Hastie,R.Tibshirani,and J.Friedman,The Elements of Statistical Learning:Data Mining,Inference and Prediction(2nd ed.).New York:Springer,2009.
[20]A.Bemporad,A.Garulli,S.Paoletti,and A.Vicino,“Abounded-error approach to piecewise affine system identification,”TEEE Transactions on Automatic Control,vol.50,no.10,2005.
[21]N.Ozay,M.Sznaier,C.M.Lagoa,and O.I.Camps,“Asparsification approach to set membership identification of switched affine systems,”IEEE Transactions on Automatic Control,vol.57,no.3,pp.634-648,2012.
[22]C.Feng,C.M.Lagoa,and M.Sznaier,“Hybrid system identification via sparse polynomial optimization,”in 2010 American Control Conference.New York:IEEE,2010,pp.160-165.
[23]L.Bako,“Identification of switched linear systems via sparse optimization,”Automatica,vol.47,no.4,pp.668-677,2011.
[24]N.Ozay,C.Lagoa,and M.Sznaier,“Robust identification of switched affine systems via moments-based convex optimization,”in Proceedings of the 48th IEEE Conference on Decision and Control,2009,pp.4686-4691.
[25]R.Vidal,S.Soatto,Y.Ma,and S.Sastry,“An algebraic geometric approach to the identification of a class of linear hybrid systems,”in Proceedings of 42nd IEEE Conference On Decision And Control,Vols 1-6.New York,2003,pp.167-172.
[26]R.Vidal,“Recursive identification of switched arx systems,”Automatica,vol.44,no.9,pp.2274-2287,2008.
[27]A.Juloski,S.Wieland,and W.Heemels,“A bayesian approach to identification of hybrid systems,”IEEE Transactions on Automatic Control,vol.50,no.10,2005.
[28]A.Doucet,N.J.Gordon,and V.Krishnamurthy,“Particle filters for state estimation of jump markov linear systems,”IEEETransactions On Signal Processing,vol.49,no.3,pp.613-624,2001.
[29]H.Nakada,K.Takaba,and T.Katayama,“Identification of piecewise affine systems based on statistical clustering technique,”Automatica,vol.41,no.5,2005.
[30]A.Logothetis and V.Krishnamurthy,“Expectation maximization algorithms for map estimation of jump markov linear systems,”IEEE Transactions On Signal Processing,vol.47,no.8,pp.2139-2156,1999.
[31]T.Routtenberg and J.Tabrikian,“Mimo-ar system identification and blind source separation for gmm-distributed sources,”IEEE Transactions on Signal Processing,vol.57,no.5,pp.1717-1730,2009.
[32]M.Viberg,“Subspace-based methods for the identification of linear time-invariant systems,”Automatica,vol.31,no.12,pp.1835-1851,1995.
[33]H.A.T.Mc Kelvey and L.Ljung,“Subspace-based multivariable system identification from frequency response data,”IEEETransations on Automatic Control,vol.41,no.7,July 1996.
[34]L.Tong and S.Perreau,“Multichannel blind identification:From subspace to maximum likelihood methods,”Proceedings Of The IEEE,vol.86,no.10,pp.1951-1968,1998.
[35]J.Liang and Z.Ding,“Blind mimo system identification based on cumulant subspace decomposition,”IEEE Transactions On Signal Processing,vol.51,no.6,pp.1457-1468,2003.
[36]S.An,J.H.Manton,and Y.Hua,“A sequential subspace method for blind identification of general fir mimo channels,”IEEE Transactions on Signal Processing,vol.53,no.10,pp.3906-3910,2005.
[37]Y.N.Yu and A.P.Petropulu,“Parafac-based blind estimation of possibly underdetermined convolutive mimo systems,”IEEE Transactions On Signal Processing,vol.56,no.1,pp.111-124,2008.
[38]C.Aykanat,A.Pinar,and U.V.Catalyurek,“Permuting sparse rectangular matrices into block-diagonal form,”SIAMJournal On Scientific Computing,vol.25,no.6,pp.1860-1879,2004.
[39]U.von Luxburg,“A tutorial on spectral clustering,”Statistics And Computing,vol.17,no.4,pp.395-416,2007.
[40]J.B.Shi and J.Malik,“Normalized cuts and image segmentation,”IEEE Transactions On Pattern Analysis And Machine Intelligence,vol.22,no.8,pp.888-905,2000.
[2]Y.D.Ji and H.J.Chizeck,“Controllability,stabilizability,and continuous-time markovian jump linear quadratic control,”IEEE Transactions on Automatic Control,vol.35,no.7,pp.777-788,1990.
[3]P.Grieder,M.Kvasnica,M.Baotic,and M.Morati,“Stabilizing low complexity feedback control of constrained piecewise affine systems,”Automatica,vol.41,no.10,pp.1683-1694,2005.
[4]L.Habets,P.J.Collins,and J.H.van Schuppen,“Reachability and control synthesis for piecewise-affine hybrid systems on simplices,”IEEE Transactions On Automatic Control,vol.51,no.6,pp.938-948,2006.
[5]M.Zhong,H.Ye,P.Shi,and G.Wang,“Fault detection for markovian jump systems,”IEE Proceedings Control Theory and Applications,vol.152,no.4,pp.397-402,2005.
[6]N.Meskin and K.Khorasani,“A geometric approach to fault detection and isolation of continuous-time markovian jump linear systems,”IEEE Transactions on Automatic Control,vol.55,no.6,pp.1343-1357,2010.
[7]L.G.Wu,X.M.Yao,and W.X.Zheng,“Generalized h-2 fault detection for two-dimensional markovian jump systems,”Automatica,vol.48,no.8,pp.1741-1750,2012.
[8]A.Guha and A.Biswas,“An overview of modeling techniques for hybrid brain data,”Statistica Sinica,vol.18,no.4,pp.1311-1340,2008.
[9]R.Vidal,M.Yi,and S.Sastry,“Generalized principal component analysis(gpca),”IEEE Transactions on Pattern Analysis and Machine Intelligence,vol.27,no.12,pp.1945-1959,2005.
[10]P.Turaga,R.Chellappa,V.S.Subrahmanian,and O.Udrea,“Machine recognition of human activities:A survey,”IEEETransactions On Circuits And Systems For Video Technology,vol.18,no.11,pp.1473-1488,2008.
[11]R.Vidal,“Subspace clustering,”IEEE Signal Processing Magazine,vol.28,no.2,pp.52-68,2011.
[12]A.Doucet,A.Logothetis,and V.Krishnamurthy,“Stochastic sampling algorithms for state estimation of jump markov linear systems,”IEEE Transactions on Automatic Control,vol.45,no.2,pp.188-202,2000.
[13]C.Biao and T.Lang,“Traffic-aided multiuser detection for random-access cdma networks,”IEEE Transactions on Signal Processing,vol.49,no.7,pp.1570-1580,2001.
[14]A.Juloski,W.Heemels,G.Ferrari-Trecate,R.Vidal,S.Paoletti,and J.Niessen,“Comparison of four procedures for the identification of hybrid systems,”in Hybrid systems:computation and control:8th international workshop(HSCC’2005),Zurich,Switzerland,2005,pp.354-369.
[15]S.Paoletti,A.L.Juloski,G.Ferrari-Trecate,and R.Vidal,“I-dentification of hybrid systems-a tutorial,”European Journal Of Control,vol.13,no.2-3,pp.242-260,2007.
[16]G.Ferrari-Trecate,M.Muselli,D.Liberati,and M.Morari,“Aclustering technique for the identification of piecewise affine systems,”Automatica,vol.39,no.2,2003.
[17]M.E.Gegundez,J.Aroba,and J.M.Bravo,“Identification of piecewise affine systems by means of fuzzy clustering and competitive learning,”Engineering Applications Of Artificial Intelligence,vol.21,no.8,pp.1321-1329,2008.
[18]L.Li,W.Dong,Y.D.Ji,and Z.K.Zhang,“An improved parameter identification approach for piecewise affine model,”Control Engineering Practice,vol.21,no.1,pp.54-64,2013.
[19]T.Hastie,R.Tibshirani,and J.Friedman,The Elements of Statistical Learning:Data Mining,Inference and Prediction(2nd ed.).New York:Springer,2009.
[20]A.Bemporad,A.Garulli,S.Paoletti,and A.Vicino,“Abounded-error approach to piecewise affine system identification,”TEEE Transactions on Automatic Control,vol.50,no.10,2005.
[21]N.Ozay,M.Sznaier,C.M.Lagoa,and O.I.Camps,“Asparsification approach to set membership identification of switched affine systems,”IEEE Transactions on Automatic Control,vol.57,no.3,pp.634-648,2012.
[22]C.Feng,C.M.Lagoa,and M.Sznaier,“Hybrid system identification via sparse polynomial optimization,”in 2010 American Control Conference.New York:IEEE,2010,pp.160-165.
[23]L.Bako,“Identification of switched linear systems via sparse optimization,”Automatica,vol.47,no.4,pp.668-677,2011.
[24]N.Ozay,C.Lagoa,and M.Sznaier,“Robust identification of switched affine systems via moments-based convex optimization,”in Proceedings of the 48th IEEE Conference on Decision and Control,2009,pp.4686-4691.
[25]R.Vidal,S.Soatto,Y.Ma,and S.Sastry,“An algebraic geometric approach to the identification of a class of linear hybrid systems,”in Proceedings of 42nd IEEE Conference On Decision And Control,Vols 1-6.New York,2003,pp.167-172.
[26]R.Vidal,“Recursive identification of switched arx systems,”Automatica,vol.44,no.9,pp.2274-2287,2008.
[27]A.Juloski,S.Wieland,and W.Heemels,“A bayesian approach to identification of hybrid systems,”IEEE Transactions on Automatic Control,vol.50,no.10,2005.
[28]A.Doucet,N.J.Gordon,and V.Krishnamurthy,“Particle filters for state estimation of jump markov linear systems,”IEEETransactions On Signal Processing,vol.49,no.3,pp.613-624,2001.
[29]H.Nakada,K.Takaba,and T.Katayama,“Identification of piecewise affine systems based on statistical clustering technique,”Automatica,vol.41,no.5,2005.
[30]A.Logothetis and V.Krishnamurthy,“Expectation maximization algorithms for map estimation of jump markov linear systems,”IEEE Transactions On Signal Processing,vol.47,no.8,pp.2139-2156,1999.
[31]T.Routtenberg and J.Tabrikian,“Mimo-ar system identification and blind source separation for gmm-distributed sources,”IEEE Transactions on Signal Processing,vol.57,no.5,pp.1717-1730,2009.
[32]M.Viberg,“Subspace-based methods for the identification of linear time-invariant systems,”Automatica,vol.31,no.12,pp.1835-1851,1995.
[33]H.A.T.Mc Kelvey and L.Ljung,“Subspace-based multivariable system identification from frequency response data,”IEEETransations on Automatic Control,vol.41,no.7,July 1996.
[34]L.Tong and S.Perreau,“Multichannel blind identification:From subspace to maximum likelihood methods,”Proceedings Of The IEEE,vol.86,no.10,pp.1951-1968,1998.
[35]J.Liang and Z.Ding,“Blind mimo system identification based on cumulant subspace decomposition,”IEEE Transactions On Signal Processing,vol.51,no.6,pp.1457-1468,2003.
[36]S.An,J.H.Manton,and Y.Hua,“A sequential subspace method for blind identification of general fir mimo channels,”IEEE Transactions on Signal Processing,vol.53,no.10,pp.3906-3910,2005.
[37]Y.N.Yu and A.P.Petropulu,“Parafac-based blind estimation of possibly underdetermined convolutive mimo systems,”IEEE Transactions On Signal Processing,vol.56,no.1,pp.111-124,2008.
[38]C.Aykanat,A.Pinar,and U.V.Catalyurek,“Permuting sparse rectangular matrices into block-diagonal form,”SIAMJournal On Scientific Computing,vol.25,no.6,pp.1860-1879,2004.
[39]U.von Luxburg,“A tutorial on spectral clustering,”Statistics And Computing,vol.17,no.4,pp.395-416,2007.
[40]J.B.Shi and J.Malik,“Normalized cuts and image segmentation,”IEEE Transactions On Pattern Analysis And Machine Intelligence,vol.22,no.8,pp.888-905,2000.