类多变量方程误差类系统的递阶多新息辨识方法
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摘要
根据递阶辨识原理,研究了类多变量方程误差系统和类多变量方程误差ARMA系统递阶随机梯度方法和递阶梯度迭代方法、递阶最小二乘方法和递阶最小二乘迭代方法.进一步利用多新息辨识理论,推导了递阶多新息梯度辨识方法和递阶多新息最小二乘辨识方法.为减小计算量,推导了基于滤波的类多变量方程误差ARMA系统递阶辨识方法和递阶多新息辨识方法.讨论了几个典型辨识算法的计算量,并给出了计算参数估计的步骤.
According to the hierarchical identification principle,this paper presents the hierarchical stochastic gradient algorithms and the hierarchical gradient based iterative algorithms,the hierarchical least squares algorithms and the hierarchical least squares based iterative algorithms for multivariable equation-error-like systems and multivariable equation-error ARMA-like systems,and further derives the hierarchical multi-innovation gradient algorithms and the hierarchical multi-innovation least squares algorithms.In order to reduce computational burdens,this paper derives the filtering based hierarchical identification algorithms and the filtering based hierarchical multi-innovation identification algorithms for multivariable equation-error ARMA-like systems using the filtering technique. Finally,the computational efficiency and the computational steps of some typical identification algorithms are discussed.
According to the hierarchical identification principle,this paper presents the hierarchical stochastic gradient algorithms and the hierarchical gradient based iterative algorithms,the hierarchical least squares algorithms and the hierarchical least squares based iterative algorithms for multivariable equation-error-like systems and multivariable equation-error ARMA-like systems,and further derives the hierarchical multi-innovation gradient algorithms and the hierarchical multi-innovation least squares algorithms.In order to reduce computational burdens,this paper derives the filtering based hierarchical identification algorithms and the filtering based hierarchical multi-innovation identification algorithms for multivariable equation-error ARMA-like systems using the filtering technique. Finally,the computational efficiency and the computational steps of some typical identification algorithms are discussed.
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,2014 DING Feng.System identification:Performance analysis for identification methods[M].Beijing:Science Press,2014
[3]丁锋.系统辨识(1):辨识导引[J].南京信息工程大学学报:自然科学版,2011,3(1):1-22DING Feng.System identification.Part A:Introduction to the identification[J].Journal of Nanjing University of Information Science and Technology:Natural Science Edition,2011,3(1):1-22
[4]丁锋.系统辨识(2):系统描述的基本模型[J].南京信息工程大学学报:自然科学版,2011,3(2):97-117DING Feng.System identification.Part B:Basic models for system description[J].Journal of Nanjing University of Information Science and Technology:Natural Science Edition,2011,3(2):97-117
[5]丁锋.系统辨识(3):辨识精度与辨识基本问题[J].南京信息工程大学学报:自然科学版,2011,3(3):193-226DING Feng.System identification.Part C:Identification accuracy and basic problems[J].Journal of Nanjing University of Information Science and Technology:Natural Science Edition,2011,3(3):193-226
[6]丁锋.系统辨识(4):辅助模型辨识思想与方法[J].南京信息工程大学学报:自然科学版,2011,3(4):289-318DING Feng.System identification.Part D:Auxiliary model identification idea and methods[J].Journal of Nanjing University of Information Science and Technology:Natural Science Edition,2011,3(4):289-318
[7]丁锋.系统辨识(5):迭代搜索原理与辨识方法[J].南京信息工程大学学报:自然科学版,2011,3(6):481-510DING Feng.System identification.Part E:Iterative search principle and identification methods[J].Journal of Nanjing University of Information Science and Technology:Natural Science Edition,2011,3(6):481-510
[8]丁锋.系统辨识(6):多新息辨识理论与方法[J].南京信息工程大学学报:自然科学版,2012,4(1):1-28DING Feng.System identification.Part F:Multi-innovation identification theory and methods[J].Journal of Nanjing University of Information Science and Technology:Natural Science Edition,2012,4(1):1-28
[9]丁锋.系统辨识(7):递阶辨识原理与方法[J].南京信息工程大学学报:自然科学版,2012,4(2):97-124DING Feng.System identification.Part G:Hierarchical identification principle and methods[J].Journal of Nanjing University of Information Science and Technology:Natural Science Edition,2012,4(2):97-124
[10]丁锋.系统辨识(8):耦合辨识概念与方法[J].南京信息工程大学学报:自然科学版,2012,4(3):193-212DING Feng.System identification.Part H:Coupling identification concept and methods[J].Journal of Nanjing University of Information Science and Technology:Natural Science Edition,2012,4(3):193-212
[11]丁锋.辨识方法的计算效率(1):递推算法[J].南京信息工程大学学报:自然科学版,2012,4(4):289-300DING Feng.Computational efficiency of the identification methods.Part A:Recursive algorithms[J].Journal of Nanjing University of Information Science and Technology:Natural Science Edition,2012,4(4):289-300
[12]丁锋.辨识方法的计算效率(2):迭代算法[J].南京信息工程大学学报:自然科学版,2012,4(5):385-401DING Feng.Computational efficiency of the identification methods.Part B:Iterative algorithms[J].Journal of Nanjing University of Information Science and Technology:Natural Science Edition,2012,4(5):385-401
[13]丁锋.辨识方法的计算效率(3):信息向量耦合算法[J].南京信息工程大学学报:自然科学版,2012,4(6):481-495DING Feng.Computational efficiency of the identification methods.Part C:Coupled information vector algorithms[J].Journal of Nanjing University of Information Science and Technology:Natural Science Edition,2012,4(6):481-495
[14]丁锋,汪菲菲.多元系统耦合多新息随机梯度类辨识方法[J].南京信息工程大学学报:自然科学版,2014,6(1):1-16DING Feng,WANG Feifei.Coupled multi-innovation stochastic gradient type identification methods for multivariate systems[J].Journal of Nanjing University of Information Science and Technology:Natural Science Edition,2014,6(1):1-16
[15]丁锋,汪菲菲,汪学海.多元伪线性回归系统部分耦合多新息随机梯度类辨识方法[J].南京信息工程大学学报:自然科学版,2014,6(2):97-112DING Feng,WANG Feifei,WANG Xuehai.Partially Coupled multi-innovation stochastic gradient type identification methods for multivariate pseudo-linear regressive systems[J].Journal of Nanjing University of Information Science and Technology:Natural Science Edition,2014,6(2):97-112
[16]丁锋,汪菲菲,汪学海.类多变量输出误差系统的耦合多新息辨识方法[J].南京信息工程大学学报:自然科学版,2014,6(3):193-210DING Feng,WANG Feifei,WANG Xuehai.Coupled multi-innovation identification methods for multivariable output-error-like systems[J].Journal of Nanjing University of Information Science and Technology:Natural Science Edition,2014,6(3):193-210
[17]丁锋,汪菲菲,汪学海.多变量方程误差类系统的部分耦合迭代辨识方法[J].南京信息工程大学学报:自然科学版,2014,6(4):289-305DING Feng,WANG Feifei,WANG Xuehai.Partially coupled iterative identification methods for multivariable equation error type systems[J].Journal of Nanjing University of Information Science and Technology:Natural Science Edition,2014,6(4):289-305
[18]丁锋,杨家本.大系统的递阶辨识[J].自动化学报,1999,25(5):647-654DING Feng,YANG Jiaben.Hierarchical identification of large scale systems[J].Acta Automatica Sinica,1999,25(5):647-654
[19]Ding F,Chen T.Hierarchical gradient-based identification of multivariable discrete-time systems[J].Automatica,2005,41(2):315-325
[20]Ding F,Chen T.Hierarchical least squares identification methods for multivariable systems[J].IEEE Transactions on Automatic Control,2005,50(3):397-402
[21]Ding F,Chen T.Gradient based iterative algorithms for solving a class of matrix equations[J].IEEE Transactions on Automatic Control,2005,50(8):1216-1221
[22]Ding F,Chen T.Iterative least squares solutions of coupled Sylvester matrix equations[J].Systems and Control Letters,2005,54(2):95-107
[23]Ding F,Chen T.On iterative solutions of general coupled matrix equations[J].SIAM Journal on Control and Optimization,2006,44(6):2269-2284
[24]Ding F,Liu X P,Ding J.Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle[J].Applied Mathematics and Computation,2008,197(1):41-50
[25]Ding F,Zhang H M.Gradient-based iterative algorithm for a class of the coupled matrix equations related to control systems[J].IET Control Theory and Applications 2014,8.doi:10.1049/iet-cta.2013.1044
[26]Han H Q,Xie L,Ding F,et al.Hierarchical least squares based iterative identification for multivariable systems with moving average noises[J].Mathematical and Computer Modelling,2010,51(9/10):1213-1220
[27]ZNZhang Z N,Ding F,Liu X G.Hierarchical gradient based iterative parameter estimation algorithm for multivariable output error moving average systems[J].Computers and Mathematics with Applications,2011,61(3):672-682
[28]Ding F,Chen T.Hierarchical identification of lifted statespace models for general dual-rate systems[J].IEEE Transactions on Circuits and Systems.I:Regular Papers,2005,52(6):1179-1187
[29]丁锋,萧德云.多变量系统状态空间模型的递阶辨识[J].控制与决策,2005,20(8):848-853,859DING Feng,XIAO Deyun.Hierarchical identification of state space models for multivariable systems[J].Control and Decision,2005,20(8):848-853,859
[30]Wang L Y,Ding F,Liu X P.Consistency of HLS estimation algorithms for MIMO ARX-like systems[J].Applied Mathematics and Computation,2007,190(2):1081-1093
[31]Ding F,Qiu L,Chen T.Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems[J].Automatica,2009,45(2):324-332
[32]Ding J,Ding F,Liu X P,et al.Hierarchical least squares identification for linear SISO systems with dual-rate sampled-data[J].IEEE Transactions on Automatic Control,2011,56(11):2677-2683
[33]Ding F.Hierarchical multi-innovation stochastic gradient algorithm for Hammerstein nonlinear system modeling[J].Applied Mathematical Modelling,2013,37(4):1694-1704
[34]Liu Y J,Ding F,Shi Y.An efficient hierarchical identification method for general dual-rate sampled-data systems[J].Automatica,2014,50(3):962-970.
[35]丁锋,谢新民,方崇智.时变系统辨识的多新息方法[J].自动化学报,1996,22(1):85-91DING Feng,XIE Xinmin,FANG Chongzhi.Multiinnovation identification methods for time-varying systems[J].Acta Automatica Sinica,1996,22(1):85-91
[36]Ding F,Chen T.Performance analysis of multi-innovation gradient type identification methods[J].Automatica,2007,43(1):1-14
[37]Ding F,Liu X P,Liu G.Multi-innovation least squares identification for system modeling[J].IEEE Transactions on Systems,Man,and Cybernetics,Part B:Cybernetics,2010,40(3):767-778
[38]Ding F,Liu G,Liu X P.Parameter estimation with scarce measurements[J].Automatica,2011,47(8):1646-1655
[39]丁锋,萧德云,丁韬.多新息随机梯度辨识方法[J].控制理论与应用,2003,20(6):870-874DING Feng,XIAO Deyun,DING Tao.Multi-innovation stochastic gradient identification methods[J].Control Theory and Application,2003,20(6):870-874
[40]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
[41]Liu Y J,Yu L,Ding F.Multi-innovation extended stochastic gradient algorithm and its performance analysis[J].Circuits,Systems and Signal Processing,2010,29(4):649-667
[42]Ding F.Several multi-innovation identification methods[J].Digital Signal Processing,2010,20(4):1027-1039
[43]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
[2]丁锋.系统辨识:辨识方法性能分析[M].北京:科学出版社,2014 DING Feng.System identification:Performance analysis for identification methods[M].Beijing:Science Press,2014
[3]丁锋.系统辨识(1):辨识导引[J].南京信息工程大学学报:自然科学版,2011,3(1):1-22DING Feng.System identification.Part A:Introduction to the identification[J].Journal of Nanjing University of Information Science and Technology:Natural Science Edition,2011,3(1):1-22
[4]丁锋.系统辨识(2):系统描述的基本模型[J].南京信息工程大学学报:自然科学版,2011,3(2):97-117DING Feng.System identification.Part B:Basic models for system description[J].Journal of Nanjing University of Information Science and Technology:Natural Science Edition,2011,3(2):97-117
[5]丁锋.系统辨识(3):辨识精度与辨识基本问题[J].南京信息工程大学学报:自然科学版,2011,3(3):193-226DING Feng.System identification.Part C:Identification accuracy and basic problems[J].Journal of Nanjing University of Information Science and Technology:Natural Science Edition,2011,3(3):193-226
[6]丁锋.系统辨识(4):辅助模型辨识思想与方法[J].南京信息工程大学学报:自然科学版,2011,3(4):289-318DING Feng.System identification.Part D:Auxiliary model identification idea and methods[J].Journal of Nanjing University of Information Science and Technology:Natural Science Edition,2011,3(4):289-318
[7]丁锋.系统辨识(5):迭代搜索原理与辨识方法[J].南京信息工程大学学报:自然科学版,2011,3(6):481-510DING Feng.System identification.Part E:Iterative search principle and identification methods[J].Journal of Nanjing University of Information Science and Technology:Natural Science Edition,2011,3(6):481-510
[8]丁锋.系统辨识(6):多新息辨识理论与方法[J].南京信息工程大学学报:自然科学版,2012,4(1):1-28DING Feng.System identification.Part F:Multi-innovation identification theory and methods[J].Journal of Nanjing University of Information Science and Technology:Natural Science Edition,2012,4(1):1-28
[9]丁锋.系统辨识(7):递阶辨识原理与方法[J].南京信息工程大学学报:自然科学版,2012,4(2):97-124DING Feng.System identification.Part G:Hierarchical identification principle and methods[J].Journal of Nanjing University of Information Science and Technology:Natural Science Edition,2012,4(2):97-124
[10]丁锋.系统辨识(8):耦合辨识概念与方法[J].南京信息工程大学学报:自然科学版,2012,4(3):193-212DING Feng.System identification.Part H:Coupling identification concept and methods[J].Journal of Nanjing University of Information Science and Technology:Natural Science Edition,2012,4(3):193-212
[11]丁锋.辨识方法的计算效率(1):递推算法[J].南京信息工程大学学报:自然科学版,2012,4(4):289-300DING Feng.Computational efficiency of the identification methods.Part A:Recursive algorithms[J].Journal of Nanjing University of Information Science and Technology:Natural Science Edition,2012,4(4):289-300
[12]丁锋.辨识方法的计算效率(2):迭代算法[J].南京信息工程大学学报:自然科学版,2012,4(5):385-401DING Feng.Computational efficiency of the identification methods.Part B:Iterative algorithms[J].Journal of Nanjing University of Information Science and Technology:Natural Science Edition,2012,4(5):385-401
[13]丁锋.辨识方法的计算效率(3):信息向量耦合算法[J].南京信息工程大学学报:自然科学版,2012,4(6):481-495DING Feng.Computational efficiency of the identification methods.Part C:Coupled information vector algorithms[J].Journal of Nanjing University of Information Science and Technology:Natural Science Edition,2012,4(6):481-495
[14]丁锋,汪菲菲.多元系统耦合多新息随机梯度类辨识方法[J].南京信息工程大学学报:自然科学版,2014,6(1):1-16DING Feng,WANG Feifei.Coupled multi-innovation stochastic gradient type identification methods for multivariate systems[J].Journal of Nanjing University of Information Science and Technology:Natural Science Edition,2014,6(1):1-16
[15]丁锋,汪菲菲,汪学海.多元伪线性回归系统部分耦合多新息随机梯度类辨识方法[J].南京信息工程大学学报:自然科学版,2014,6(2):97-112DING Feng,WANG Feifei,WANG Xuehai.Partially Coupled multi-innovation stochastic gradient type identification methods for multivariate pseudo-linear regressive systems[J].Journal of Nanjing University of Information Science and Technology:Natural Science Edition,2014,6(2):97-112
[16]丁锋,汪菲菲,汪学海.类多变量输出误差系统的耦合多新息辨识方法[J].南京信息工程大学学报:自然科学版,2014,6(3):193-210DING Feng,WANG Feifei,WANG Xuehai.Coupled multi-innovation identification methods for multivariable output-error-like systems[J].Journal of Nanjing University of Information Science and Technology:Natural Science Edition,2014,6(3):193-210
[17]丁锋,汪菲菲,汪学海.多变量方程误差类系统的部分耦合迭代辨识方法[J].南京信息工程大学学报:自然科学版,2014,6(4):289-305DING Feng,WANG Feifei,WANG Xuehai.Partially coupled iterative identification methods for multivariable equation error type systems[J].Journal of Nanjing University of Information Science and Technology:Natural Science Edition,2014,6(4):289-305
[18]丁锋,杨家本.大系统的递阶辨识[J].自动化学报,1999,25(5):647-654DING Feng,YANG Jiaben.Hierarchical identification of large scale systems[J].Acta Automatica Sinica,1999,25(5):647-654
[19]Ding F,Chen T.Hierarchical gradient-based identification of multivariable discrete-time systems[J].Automatica,2005,41(2):315-325
[20]Ding F,Chen T.Hierarchical least squares identification methods for multivariable systems[J].IEEE Transactions on Automatic Control,2005,50(3):397-402
[21]Ding F,Chen T.Gradient based iterative algorithms for solving a class of matrix equations[J].IEEE Transactions on Automatic Control,2005,50(8):1216-1221
[22]Ding F,Chen T.Iterative least squares solutions of coupled Sylvester matrix equations[J].Systems and Control Letters,2005,54(2):95-107
[23]Ding F,Chen T.On iterative solutions of general coupled matrix equations[J].SIAM Journal on Control and Optimization,2006,44(6):2269-2284
[24]Ding F,Liu X P,Ding J.Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle[J].Applied Mathematics and Computation,2008,197(1):41-50
[25]Ding F,Zhang H M.Gradient-based iterative algorithm for a class of the coupled matrix equations related to control systems[J].IET Control Theory and Applications 2014,8.doi:10.1049/iet-cta.2013.1044
[26]Han H Q,Xie L,Ding F,et al.Hierarchical least squares based iterative identification for multivariable systems with moving average noises[J].Mathematical and Computer Modelling,2010,51(9/10):1213-1220
[27]ZNZhang Z N,Ding F,Liu X G.Hierarchical gradient based iterative parameter estimation algorithm for multivariable output error moving average systems[J].Computers and Mathematics with Applications,2011,61(3):672-682
[28]Ding F,Chen T.Hierarchical identification of lifted statespace models for general dual-rate systems[J].IEEE Transactions on Circuits and Systems.I:Regular Papers,2005,52(6):1179-1187
[29]丁锋,萧德云.多变量系统状态空间模型的递阶辨识[J].控制与决策,2005,20(8):848-853,859DING Feng,XIAO Deyun.Hierarchical identification of state space models for multivariable systems[J].Control and Decision,2005,20(8):848-853,859
[30]Wang L Y,Ding F,Liu X P.Consistency of HLS estimation algorithms for MIMO ARX-like systems[J].Applied Mathematics and Computation,2007,190(2):1081-1093
[31]Ding F,Qiu L,Chen T.Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems[J].Automatica,2009,45(2):324-332
[32]Ding J,Ding F,Liu X P,et al.Hierarchical least squares identification for linear SISO systems with dual-rate sampled-data[J].IEEE Transactions on Automatic Control,2011,56(11):2677-2683
[33]Ding F.Hierarchical multi-innovation stochastic gradient algorithm for Hammerstein nonlinear system modeling[J].Applied Mathematical Modelling,2013,37(4):1694-1704
[34]Liu Y J,Ding F,Shi Y.An efficient hierarchical identification method for general dual-rate sampled-data systems[J].Automatica,2014,50(3):962-970.
[35]丁锋,谢新民,方崇智.时变系统辨识的多新息方法[J].自动化学报,1996,22(1):85-91DING Feng,XIE Xinmin,FANG Chongzhi.Multiinnovation identification methods for time-varying systems[J].Acta Automatica Sinica,1996,22(1):85-91
[36]Ding F,Chen T.Performance analysis of multi-innovation gradient type identification methods[J].Automatica,2007,43(1):1-14
[37]Ding F,Liu X P,Liu G.Multi-innovation least squares identification for system modeling[J].IEEE Transactions on Systems,Man,and Cybernetics,Part B:Cybernetics,2010,40(3):767-778
[38]Ding F,Liu G,Liu X P.Parameter estimation with scarce measurements[J].Automatica,2011,47(8):1646-1655
[39]丁锋,萧德云,丁韬.多新息随机梯度辨识方法[J].控制理论与应用,2003,20(6):870-874DING Feng,XIAO Deyun,DING Tao.Multi-innovation stochastic gradient identification methods[J].Control Theory and Application,2003,20(6):870-874
[40]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
[41]Liu Y J,Yu L,Ding F.Multi-innovation extended stochastic gradient algorithm and its performance analysis[J].Circuits,Systems and Signal Processing,2010,29(4):649-667
[42]Ding F.Several multi-innovation identification methods[J].Digital Signal Processing,2010,20(4):1027-1039
[43]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