辅助模型辨识方法(6):性能分析
|
摘要
辨识方法的性能分析是系统辨识领域的重要而困难的研究课题.新的辨识方法一诞生,就伴随着收敛性分析.辅助模型辨识是辨识的一个分支,辅助模型辨识方法已成为一大类辨识方法族,关于其收敛性也提出了许多课题.本文研究了输出误差系统辅助模型随机梯度算法、辅助模型递推最小二乘算法、辅助模型多新息随机梯度算法、变间隔辅助模型随机梯度算法和变间隔辅助模型递推最小二乘算法的一致收敛性,近似分析了Box-Jenkins系统辅助模型递推广义增广最小二乘算法的性能.
Performance analysis of identification methods is the important and difficult projects in the area of system identification. Once one new identification method is born,its convergence analysis appears. The auxiliary model identification is a branch of system identification and has become a large family of identification methods,their convergence brings many projects.This paper studies the consistent convergence of the auxiliary model( AM)based stochastic gradient( SG) algorithm,the AM recursive least squares( RLS) algorithm,the AM multiinnovation SG algorithm,the interval-varying AM SG algorithm and the interval-varying AM RLS algorithm for output-error systems,and analyzes approximately the convergence of the AM recursive generalized extended least squares algorithm for Box-Jenkins systems.
Performance analysis of identification methods is the important and difficult projects in the area of system identification. Once one new identification method is born,its convergence analysis appears. The auxiliary model identification is a branch of system identification and has become a large family of identification methods,their convergence brings many projects.This paper studies the consistent convergence of the auxiliary model( AM)based stochastic gradient( SG) algorithm,the AM recursive least squares( RLS) algorithm,the AM multiinnovation SG algorithm,the interval-varying AM SG algorithm and the interval-varying AM RLS algorithm for output-error systems,and analyzes approximately the convergence of the AM recursive generalized extended least squares algorithm for Box-Jenkins systems.
引文
[1]丁锋.系统辨识新论[M].北京:科学出版社,2013DING Feng.System identification:New theory and methods[M].Beijing:Science Press,2013
[2]丁锋.系统辨识:辨识方法性能分析[M].北京:科学出版社,2014DING Feng.System identification:Performance analysis for identification methods[M].Beijing:Science Press,2014
[3]丁锋.系统辨识:多新息辨识理论与方法[M].北京:科学出版社,2016DING Feng.System identification:Multi-innovation identification theory and methods[M].Beijing:Science Press,2016
[4]丁锋.系统辨识:辅助模型辨识思想与方法[M].北京:科学出版社,2017DING Feng.System identification:Auxiliary model identification idea and methods[M].Beijing:Science Press,2017
[5]丁锋.方程误差类系统的多新息辨识方法[J].南京信息工程大学学报(自然科学版),2015,7(5):385-407DING Feng.Multi-innovation identification methods for equation-error type systems[J].Journal of Nanjing University of Information Science and Technology(Natural Science Edition),2015,7(5):385-407
[6]丁锋.系统辨识算法复杂性、收敛性、计算效率研究[J].控制与决策,2016,31(10):1729-1741DING Feng.Complexity,convergence and computational efficiency for system identification algorithms[J].Control and Decision,2016,31(10):1729-1741
[7]Ding F,Chen T.Modeling and identification for multirate systems[J].Acta Automatica Sinica,2005,31(1):105-122
[8]丁锋,杨慧中,纪志成.时变系统辨识方法及其收敛定理[J].江南大学学报(自然科学版),2006,5(1):115-126DING Feng,YANG Huizhong JI Zhicheng.Time-varying system identification methods and convergence theorems[J].Journal of Southern Yangtze University(Natural Science Edition),2006,5(1):115-126
[9]Ding F,Chen T.Combined parameter and output estimation of dual-rate systems using an auxiliary model[J].Automatica,2004,40(10):1739-1748
[10]Ding F,Chen T.Parameter estimation of dual-rate stochastic systems by using an output error method[J].IEEE Transactions on Automatic Control,2005,50(9):1436-1441
[11]Duan H H,Jia J,Ding R F.Two-stage recursive least squares parameter estimation algorithm for output error models[J].Mathematical and Computer Modelling,2012,55(3-4):1151-1159
[12]丁锋.基于输出估计的多输入系统随机梯度估计算法[J].南京信息工程大学学报(自然科学版),2010,2(6):481-488DING Feng.Stochastic gradient estimation algorithm for multiple-input systems based on the output estimation[J].Journal of Nanjing University of Information Science and Technology(Natural Science Edition),2010,2(6):481-488
[13]Wang D Q,Ding F.Performance analysis of the auxiliary models based multi-innovation stochastic gradient estimation algorithm for output error systems[J].Digital Signal Processing,2010,20(3):750-762
[14]Ding F,Liu X P,Liu G.Gradient based and least-squares based iterative identification methods for OE and OEMAsystems[J].Digital Signal Processing,2010,20(3):664-677
[15]王冬青.基于辅助模型的递推增广最小二乘辨识方法[J].控制理论与应用,2009,26(1):51-56WANG Dongqing.Recursive extended least squares identification method based on auxiliary models[J].Control Theory and Applications,2009,26(1):51-56
[16]Ding F,Liu X P,Liu G.Auxiliary model based multi-innovation extended stochastic gradient parameter estimation with colored measurement noises[J].Signal Processing,2009,89(10):1883-1890
[17]Wang D Q.Least squares-based recursive and iterative estimation for output error moving average systems using data filtering[J].IET Control theory and Applications,2011,5(14):1648-1657
[18]Ding F,Wang Y J,Ding J.Recursive least squares parameter identification for systems with colored noise using the filtering technique and the auxiliary model[J].Digital Signal Processing,2015,37:100-108
[19]Ding F,Duan H H.Two-stage parameter estimation algorithms for Box-Jenkins systems[J].IET Signal Processing,2013,7(2):176-184
[20]Liu Y J,Wang D Q,Ding F.Least-squares based iterative algorithms for identifying Box-Jenkins models with finite measurement data[J].Digital Signal Processing,2010,20(5):1458-1467
[21]Wang D Q,Yang G W,Ding F.Gradient-based iterative parameter estimation for Box-Jenkins systems with finite measurement data[J].Computers and Mathematics with Applications,2010,60(5):1200-1208
[22]Wang X H,Ding F.Convergence of the auxiliary model based multi-innovation generalized extended stochastic gradient algorithm for Box-Jenkins systems[J].Nonlinear Dynamics,2015,82(1-2):269-280
[23]丁锋,郭兰杰.线性参数系统的多新息辨识方法[J].南京信息工程大学学报(自然科学版),2015,7(4):289-312DING Feng,GUO Lanjie.Multi-innovation identification methods for linear-parameter systems[J].Journal of Nanjing University of Information Science and Technology(Natural Science Edition),2015,7(4):289-312
[24]Mao Y W,Ding F.Data filtering-based multi-innovation stochastic gradient algorithm for nonlinear output error autoregressive systems[J].Circuits,Systems and Signal Processing,2016,35(2):651-667
[25]Mao Y W,Ding F.Parameter estimation for nonlinear systems by using the data filtering and the multi-innovation identification theory[J].International Journal of Computer Mathematics,2016,93(11):1869-1885
[26]Hu P P,Ding F,Sheng J.Auxiliary model based least squares parameter estimation algorithm for feedback nonlinear systems using the hierarchical identification principle[J].Journal of the Franklin Institute,2013,350(10),3248-3259
[27]Hu P P,Ding F.Multistage least squares based iterative estimation for feedback nonlinear systems with moving average noises using the hierarchical identification principle[J].Nonlinear Dynamics,2013,73(1-2),583-592
[28]Ding F,Liu G,Liu X P.Parameter estimation with scarce measurements[J].Automatica,2011,47(8):1646-1655
[29]Ding F,Ding J.Least squares parameter estimation with irregularly missing data[J].International Journal of Adaptive Control and Signal Processing,2010,24(7):540-553
[30]丁锋,谢新民.多变量系统的辅助模型辨识算法[J].清华大学学报(自然科学版),1992,32(4):100-106DING Feng,XIE Xinmin.Auxiliary model identification method for multivariable systems[J].Journal of Tsinghua University:Science and Technology,1992,32(4):100-106
[31]丁锋.多变量系统的辅助模型辨识方法的收敛性分析[J].控制理论与应用,1997,14(2):192-200DING Feng.Convergence analysis of auxiliary model identification algorithms for multivariable systems[J].Control Theory and Applications,1997,14(2):192-200
[32]Ding F,Liu X P.Auxiliary model based stochastic gradient algorithm for multivariable output error systems[J].Acta Automatica Sinica,2010,36(7):993-998
[33]Ding F,Chen H B,Li M.Multi-innovation least squares identification methods based on the auxiliary model for MISO systems[J].Applied Mathematics and Computation,2007,187(2):658-668
[34]Liu Y J,Xie L,Ding F.An auxiliary model recursive least squares parameter estimation algorithm for non-uniformly sampled multirate systems[J].Proceedings of the Institution of Mechanical Engineers,Part I:Journal of Systems and Control Engineering,2009,223(4):445-454
[35]Xie L,Liu Y J,Yang H Z,et al.Modeling and identification for non-uniformly periodically sampled-data systems[J].IET Control Theory and Applications,2010,4(5):784-794
[36]Ding F,Gu Y.Performance analysis of the auxiliary model-based stochastic gradient parameter estimation algorithm for state space systems with one-step state delay[J].Circuits,Systems and Signal Processing,2013,32(2):585-599
[37]Ding F,Gu Y.Performance analysis of the auxiliary model-based least-squares identification algorithm for one-step state-delay systems[J].International Journal of Computer Mathematics,2012,89(15):2019-2028
[38]Ding F,Chen T,Qiu L.Bias compensation based recursive least squares identification algorithm for MISO systems[J].IEEE Transactions on Circuits and Systems,II:Express Briefs,2006,53(5):349-353
[39]Xu L.A proportional differential control method for a time-delay system using the Taylor expansion approximation[J].Applied Mathematics and Computation,2014,236:391-399
[40]Xu L.Application of the Newton iteration algorithm to the parameter estimation for dynamical systems[J].Journal of Computational and Applied Mathematics,2015,288:33-43
[41]Xu L,Chen L,Xiong W L.Parameter estimation and controller design for dynamic systems from the step responses based on the Newton iteration[J].Nonlinear Dynamics,2015,79(3):2155-2163
[42]Xu L.The damping iterative parameter identification method for dynamical systems based on the sine signal measurement[J].Signal Processing,2016,120:660-667
[43]Xie L,Yang H Z,Huang B.FIR model identification of multirate processes with random delays using EMalgorithm[J].AIChE Journal,2013,59(11):4124-4132
[44]Wang C,Tang T.Recursive least squares estimation algorithm applied to a class of linear-in-parameters output error moving average systems[J].Applied Mathematics Letters,2014,29:36-41
[45]Wang C,Tang T.Several gradient-based iterative estimation algorithms for a class of nonlinear systems using the filtering technique[J].Nonlinear Dynamics,2014,77(3):769-780
[46]Wang C,Zhu L.Parameter identification of a class of nonlinear systems based on the multi-innovation identification theory[J].Journal of the Franklin Institute,2015,352(10):4624-4637
[47]Guo L J,Wang Y J,Wang C.A recursive least squares algorithm for pseudo-linear arma systems using the auxiliary model and the filtering technique[J].Circuits,Systems and Signal Processing,2016,35(7):2655-2667
[48]Wang F F,Liu Y J,Yang E F.Least squares-based iterative identification methods for linear-in-parameters systems using the decomposition technique[J].Circuits,Systems and Signal Processing,2016,35(11):3863-3881
[49]Meng D D.Recursive least squares and multi-innovation gradient estimation algorithms for bilinear stochastic systems[J].Circuits,Systems and Signal Processing,2017.DOI:10.1007/s00034-016-0337-0
[50]Chen J,Ni Y X.Parameter identification methods for an additive nonlinear system[J].Circuits,Systems and Signal Processing,2014,33(10):3053-3064
[51]Chen J,Wang X P.Identification of Hammerstein systems with continuous nonlinearity[J].Information Processing Letters,2015,115(11):822-827
[52]Wang D Q,Zhang W.Improved least squares identification algorithm for multivariable Hammerstein systems[J].Journal of the Franklin Institute,2015,352(11):5292-5307
[53]Wang D Q.Hierarchical parameter estimation for a class of MIMO Hammerstein systems based on the reframed models[J].Applied Mathematics Letters,2016,57:13-19
[54]Li J H.Parameter estimation for Hammerstein CARARMAsystems based on the Newton iteration[J].Applied Mathematics Letters,2013,26(1):91-96
[55]Hu Y B,Liu B L,Zhou Q.A multi-innovation generalized extended stochastic gradient algorithm for outpu nonlinear autoregressive moving average systems[J].Applied Mathematics and Computation,2014,247:218-224
[2]丁锋.系统辨识:辨识方法性能分析[M].北京:科学出版社,2014DING Feng.System identification:Performance analysis for identification methods[M].Beijing:Science Press,2014
[3]丁锋.系统辨识:多新息辨识理论与方法[M].北京:科学出版社,2016DING Feng.System identification:Multi-innovation identification theory and methods[M].Beijing:Science Press,2016
[4]丁锋.系统辨识:辅助模型辨识思想与方法[M].北京:科学出版社,2017DING Feng.System identification:Auxiliary model identification idea and methods[M].Beijing:Science Press,2017
[5]丁锋.方程误差类系统的多新息辨识方法[J].南京信息工程大学学报(自然科学版),2015,7(5):385-407DING Feng.Multi-innovation identification methods for equation-error type systems[J].Journal of Nanjing University of Information Science and Technology(Natural Science Edition),2015,7(5):385-407
[6]丁锋.系统辨识算法复杂性、收敛性、计算效率研究[J].控制与决策,2016,31(10):1729-1741DING Feng.Complexity,convergence and computational efficiency for system identification algorithms[J].Control and Decision,2016,31(10):1729-1741
[7]Ding F,Chen T.Modeling and identification for multirate systems[J].Acta Automatica Sinica,2005,31(1):105-122
[8]丁锋,杨慧中,纪志成.时变系统辨识方法及其收敛定理[J].江南大学学报(自然科学版),2006,5(1):115-126DING Feng,YANG Huizhong JI Zhicheng.Time-varying system identification methods and convergence theorems[J].Journal of Southern Yangtze University(Natural Science Edition),2006,5(1):115-126
[9]Ding F,Chen T.Combined parameter and output estimation of dual-rate systems using an auxiliary model[J].Automatica,2004,40(10):1739-1748
[10]Ding F,Chen T.Parameter estimation of dual-rate stochastic systems by using an output error method[J].IEEE Transactions on Automatic Control,2005,50(9):1436-1441
[11]Duan H H,Jia J,Ding R F.Two-stage recursive least squares parameter estimation algorithm for output error models[J].Mathematical and Computer Modelling,2012,55(3-4):1151-1159
[12]丁锋.基于输出估计的多输入系统随机梯度估计算法[J].南京信息工程大学学报(自然科学版),2010,2(6):481-488DING Feng.Stochastic gradient estimation algorithm for multiple-input systems based on the output estimation[J].Journal of Nanjing University of Information Science and Technology(Natural Science Edition),2010,2(6):481-488
[13]Wang D Q,Ding F.Performance analysis of the auxiliary models based multi-innovation stochastic gradient estimation algorithm for output error systems[J].Digital Signal Processing,2010,20(3):750-762
[14]Ding F,Liu X P,Liu G.Gradient based and least-squares based iterative identification methods for OE and OEMAsystems[J].Digital Signal Processing,2010,20(3):664-677
[15]王冬青.基于辅助模型的递推增广最小二乘辨识方法[J].控制理论与应用,2009,26(1):51-56WANG Dongqing.Recursive extended least squares identification method based on auxiliary models[J].Control Theory and Applications,2009,26(1):51-56
[16]Ding F,Liu X P,Liu G.Auxiliary model based multi-innovation extended stochastic gradient parameter estimation with colored measurement noises[J].Signal Processing,2009,89(10):1883-1890
[17]Wang D Q.Least squares-based recursive and iterative estimation for output error moving average systems using data filtering[J].IET Control theory and Applications,2011,5(14):1648-1657
[18]Ding F,Wang Y J,Ding J.Recursive least squares parameter identification for systems with colored noise using the filtering technique and the auxiliary model[J].Digital Signal Processing,2015,37:100-108
[19]Ding F,Duan H H.Two-stage parameter estimation algorithms for Box-Jenkins systems[J].IET Signal Processing,2013,7(2):176-184
[20]Liu Y J,Wang D Q,Ding F.Least-squares based iterative algorithms for identifying Box-Jenkins models with finite measurement data[J].Digital Signal Processing,2010,20(5):1458-1467
[21]Wang D Q,Yang G W,Ding F.Gradient-based iterative parameter estimation for Box-Jenkins systems with finite measurement data[J].Computers and Mathematics with Applications,2010,60(5):1200-1208
[22]Wang X H,Ding F.Convergence of the auxiliary model based multi-innovation generalized extended stochastic gradient algorithm for Box-Jenkins systems[J].Nonlinear Dynamics,2015,82(1-2):269-280
[23]丁锋,郭兰杰.线性参数系统的多新息辨识方法[J].南京信息工程大学学报(自然科学版),2015,7(4):289-312DING Feng,GUO Lanjie.Multi-innovation identification methods for linear-parameter systems[J].Journal of Nanjing University of Information Science and Technology(Natural Science Edition),2015,7(4):289-312
[24]Mao Y W,Ding F.Data filtering-based multi-innovation stochastic gradient algorithm for nonlinear output error autoregressive systems[J].Circuits,Systems and Signal Processing,2016,35(2):651-667
[25]Mao Y W,Ding F.Parameter estimation for nonlinear systems by using the data filtering and the multi-innovation identification theory[J].International Journal of Computer Mathematics,2016,93(11):1869-1885
[26]Hu P P,Ding F,Sheng J.Auxiliary model based least squares parameter estimation algorithm for feedback nonlinear systems using the hierarchical identification principle[J].Journal of the Franklin Institute,2013,350(10),3248-3259
[27]Hu P P,Ding F.Multistage least squares based iterative estimation for feedback nonlinear systems with moving average noises using the hierarchical identification principle[J].Nonlinear Dynamics,2013,73(1-2),583-592
[28]Ding F,Liu G,Liu X P.Parameter estimation with scarce measurements[J].Automatica,2011,47(8):1646-1655
[29]Ding F,Ding J.Least squares parameter estimation with irregularly missing data[J].International Journal of Adaptive Control and Signal Processing,2010,24(7):540-553
[30]丁锋,谢新民.多变量系统的辅助模型辨识算法[J].清华大学学报(自然科学版),1992,32(4):100-106DING Feng,XIE Xinmin.Auxiliary model identification method for multivariable systems[J].Journal of Tsinghua University:Science and Technology,1992,32(4):100-106
[31]丁锋.多变量系统的辅助模型辨识方法的收敛性分析[J].控制理论与应用,1997,14(2):192-200DING Feng.Convergence analysis of auxiliary model identification algorithms for multivariable systems[J].Control Theory and Applications,1997,14(2):192-200
[32]Ding F,Liu X P.Auxiliary model based stochastic gradient algorithm for multivariable output error systems[J].Acta Automatica Sinica,2010,36(7):993-998
[33]Ding F,Chen H B,Li M.Multi-innovation least squares identification methods based on the auxiliary model for MISO systems[J].Applied Mathematics and Computation,2007,187(2):658-668
[34]Liu Y J,Xie L,Ding F.An auxiliary model recursive least squares parameter estimation algorithm for non-uniformly sampled multirate systems[J].Proceedings of the Institution of Mechanical Engineers,Part I:Journal of Systems and Control Engineering,2009,223(4):445-454
[35]Xie L,Liu Y J,Yang H Z,et al.Modeling and identification for non-uniformly periodically sampled-data systems[J].IET Control Theory and Applications,2010,4(5):784-794
[36]Ding F,Gu Y.Performance analysis of the auxiliary model-based stochastic gradient parameter estimation algorithm for state space systems with one-step state delay[J].Circuits,Systems and Signal Processing,2013,32(2):585-599
[37]Ding F,Gu Y.Performance analysis of the auxiliary model-based least-squares identification algorithm for one-step state-delay systems[J].International Journal of Computer Mathematics,2012,89(15):2019-2028
[38]Ding F,Chen T,Qiu L.Bias compensation based recursive least squares identification algorithm for MISO systems[J].IEEE Transactions on Circuits and Systems,II:Express Briefs,2006,53(5):349-353
[39]Xu L.A proportional differential control method for a time-delay system using the Taylor expansion approximation[J].Applied Mathematics and Computation,2014,236:391-399
[40]Xu L.Application of the Newton iteration algorithm to the parameter estimation for dynamical systems[J].Journal of Computational and Applied Mathematics,2015,288:33-43
[41]Xu L,Chen L,Xiong W L.Parameter estimation and controller design for dynamic systems from the step responses based on the Newton iteration[J].Nonlinear Dynamics,2015,79(3):2155-2163
[42]Xu L.The damping iterative parameter identification method for dynamical systems based on the sine signal measurement[J].Signal Processing,2016,120:660-667
[43]Xie L,Yang H Z,Huang B.FIR model identification of multirate processes with random delays using EMalgorithm[J].AIChE Journal,2013,59(11):4124-4132
[44]Wang C,Tang T.Recursive least squares estimation algorithm applied to a class of linear-in-parameters output error moving average systems[J].Applied Mathematics Letters,2014,29:36-41
[45]Wang C,Tang T.Several gradient-based iterative estimation algorithms for a class of nonlinear systems using the filtering technique[J].Nonlinear Dynamics,2014,77(3):769-780
[46]Wang C,Zhu L.Parameter identification of a class of nonlinear systems based on the multi-innovation identification theory[J].Journal of the Franklin Institute,2015,352(10):4624-4637
[47]Guo L J,Wang Y J,Wang C.A recursive least squares algorithm for pseudo-linear arma systems using the auxiliary model and the filtering technique[J].Circuits,Systems and Signal Processing,2016,35(7):2655-2667
[48]Wang F F,Liu Y J,Yang E F.Least squares-based iterative identification methods for linear-in-parameters systems using the decomposition technique[J].Circuits,Systems and Signal Processing,2016,35(11):3863-3881
[49]Meng D D.Recursive least squares and multi-innovation gradient estimation algorithms for bilinear stochastic systems[J].Circuits,Systems and Signal Processing,2017.DOI:10.1007/s00034-016-0337-0
[50]Chen J,Ni Y X.Parameter identification methods for an additive nonlinear system[J].Circuits,Systems and Signal Processing,2014,33(10):3053-3064
[51]Chen J,Wang X P.Identification of Hammerstein systems with continuous nonlinearity[J].Information Processing Letters,2015,115(11):822-827
[52]Wang D Q,Zhang W.Improved least squares identification algorithm for multivariable Hammerstein systems[J].Journal of the Franklin Institute,2015,352(11):5292-5307
[53]Wang D Q.Hierarchical parameter estimation for a class of MIMO Hammerstein systems based on the reframed models[J].Applied Mathematics Letters,2016,57:13-19
[54]Li J H.Parameter estimation for Hammerstein CARARMAsystems based on the Newton iteration[J].Applied Mathematics Letters,2013,26(1):91-96
[55]Hu Y B,Liu B L,Zhou Q.A multi-innovation generalized extended stochastic gradient algorithm for outpu nonlinear autoregressive moving average systems[J].Applied Mathematics and Computation,2014,247:218-224