多变量系统的耦合梯度辨识算法与性能分析
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摘要
针对多变量系统维数大、参数多、一般的辨识算法计算量大的问题,基于耦合辨识概念,推导多变量系统的耦合随机梯度算法,利用鞅收敛定理分析算法的收敛性能.算法的主要思想是将系统模型分解为多个单输出子系统,在子系统的递推辨识过程中,将每个子系统的参数估计值耦合起来.所提出算法与最小二乘算法和耦合最小二乘算法相比,具有较少的计算量,收敛速度可以通过引入遗忘因子得到改善.性能分析表明了所提出算法收敛,仿真实例验证了算法的有效性.
It is an issue that multivariable systems with high dimensions have many parameters, resulting in heavy computational costs in identification methods. Therefore, a coupled stochastic gradient algorithm is derived for multivariable systems based on the coupling identification concept. The identification model is decomposed into several single-output systems, and the parameter estimates are coupled during the subsystem identification by using the gradient search. The convergence properties are analyzed by using the martingale convergence theorem. Compared with the recursive least squares algorithm and the coupled least squares algorithm, the proposed algorithm has less computational load. The convergence rate can be improved by introducing a forgetting factor. Performance analysis verifies that the proposed algorithm converges.The simulation results show the effectiveness of the proposed algorithm.
It is an issue that multivariable systems with high dimensions have many parameters, resulting in heavy computational costs in identification methods. Therefore, a coupled stochastic gradient algorithm is derived for multivariable systems based on the coupling identification concept. The identification model is decomposed into several single-output systems, and the parameter estimates are coupled during the subsystem identification by using the gradient search. The convergence properties are analyzed by using the martingale convergence theorem. Compared with the recursive least squares algorithm and the coupled least squares algorithm, the proposed algorithm has less computational load. The convergence rate can be improved by introducing a forgetting factor. Performance analysis verifies that the proposed algorithm converges.The simulation results show the effectiveness of the proposed algorithm.
引文
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[8]Ding F.Coupled-least-squares idnetification for multivariable systems[J].IET Control Theory and Applications,2013,7(1):68-79.
[9]Liu Y J,Ding F,Shi Y.A new parameter estimation algorithm for non-uniformly multirate sampled data systems[C].American Control Conf.San Francisco,2011:84-89.
[10]Ding F,Liu G,Liu X.Partially coupled stochastic gradient identification methods for non-uniformly sampled systems[J].IEEE Trans on Automatic Control,2010,55(8):1976-1981.
[11]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):1-16.(Ding F,Wang F F.Coupled multi-innovation stochastic gradient type identification methods for multivariate systems[J].J of Nanjing University of Information Science and Technology:Natural Science Edition,2014,6(1):1-16.)
[12]丁锋.系统辨识新论[M].北京:科学出版社,2013:349-358.(Ding F.System Identification—New Theory and Methods[M].Beijing:Science Press,2013:349-358.)
[13]Goodwin G,Sin K.Adaptive filtering prediction and control[M].Englewood Cliffs:Prentice-Hall,1984:94-98.
[2]Zheng W X.On a least squares based algorithm for identification of stochastic linear systems[J].IEEE Trans on Signal Processing,1998,46(6):1631-1638.
[3]Liu Y J,Sheng J,Ding R F.Convergence of stochastic gradient estimation algorithm for multivariable ARX-like systems[J].Computers&Mathematics with Applications,2010,59(8):2615-2627.
[4]靳其兵,窦俊,李斯年,等.基于加速收敛与递阶迭代的多变量系统辨识算法[J].清华大学学报:自然科学版,2012,52(9):1194-1198.(Jin Q B,Dou J,Li S N,et al.Identification method based on accelerated convergence and hierarchical iterations for multivariable systems[J].J of Tsinghua University:Science and Technology,2012,52(9):1194-1198.)
[5]方崇智,萧德云.过程辨识[M].北京:清华大学出版社,1988:424-430.(Fang C Z,Xiao D Y.Process identification[M].Beijing:Tinghua University Press,1988:424-430.)
[6]Ding F,Chen T.Hierarchical gradient-based identification of multivariable discrete-time systems[J].Automatica,2005,41(2):315-325.
[7]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):193-212.(Ding F.System identification,Part H:Coupled identification concept and methods[J].J of Nanjing University of Information Science and Technology:Natural Science Edition,2012,4(3):193-212.)
[8]Ding F.Coupled-least-squares idnetification for multivariable systems[J].IET Control Theory and Applications,2013,7(1):68-79.
[9]Liu Y J,Ding F,Shi Y.A new parameter estimation algorithm for non-uniformly multirate sampled data systems[C].American Control Conf.San Francisco,2011:84-89.
[10]Ding F,Liu G,Liu X.Partially coupled stochastic gradient identification methods for non-uniformly sampled systems[J].IEEE Trans on Automatic Control,2010,55(8):1976-1981.
[11]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):1-16.(Ding F,Wang F F.Coupled multi-innovation stochastic gradient type identification methods for multivariate systems[J].J of Nanjing University of Information Science and Technology:Natural Science Edition,2014,6(1):1-16.)
[12]丁锋.系统辨识新论[M].北京:科学出版社,2013:349-358.(Ding F.System Identification—New Theory and Methods[M].Beijing:Science Press,2013:349-358.)
[13]Goodwin G,Sin K.Adaptive filtering prediction and control[M].Englewood Cliffs:Prentice-Hall,1984:94-98.