Hierarchical stochastic gradient parameter estimation algorithms for multivariable systems with colored noises

This paper develops a hierarchical extended stochastic gradient identification algorithms for MIMO ARMAX-like systems to deal with colored noises based on the hierarchical identification principle. The convergence performance of such algorithms is studied in detail; in particular, conditions for parameter estimation errors to converge to zero are established, which include persistent excitation of the extended information vectors and strict positive realness of the noise models. Finally, the proposed algorithms are tested on an example to show their advantages and effectiveness.

[1]  T. Lai,et al.  Recursive identification and adaptive prediction in linear stochastic systems , 1991 .

[2]  Tongwen Chen,et al.  Hierarchical least squares identification methods for multivariable systems , 2005, IEEE Transactions on Automatic Control.

[3]  T. Lai,et al.  Least Squares Estimates in Stochastic Regression Models with Applications to Identification and Control of Dynamic Systems , 1982 .

[4]  C. Z. Wei.  Adaptive Prediction by Least Squares Predictors in Stochastic Regression Models with Applications to Time Series , 1987 .

[5]  Feng Ding,et al.  Performance bounds of forgetting factor least-squares algorithms for time-varying systems with finite measurement data , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[6]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[7]  Graham C. Goodwin,et al.  Adaptive filtering prediction and control , 1984 .

[8]  Feng Ding,et al.  Identification of Hammerstein nonlinear ARMAX systems , 2005, Autom..

[9]  L. Ljung.  Consistency of the least-squares identification method , 1976 .

[10]  Feng Ding,et al.  Combined parameter and output estimation of dual-rate systems using an auxiliary model , 2004, Autom..

[11]  V. Solo.  The convergence of AML , 1979 .

[12]  Feng Ding,et al.  Hierarchical gradient-based identification of multivariable discrete-time systems , 2005, Autom..

[13]  Lei Guo,et al.  Convergence and logarithm laws of self-tuning regulators , 1995, Autom..

[14]  T. Lai,et al.  Extended least squares and their applications to adaptive control and prediction in linear systems , 1986 .

[15]  Feng Ding,et al.  Parameter estimation of dual-rate stochastic systems by using an output error method , 2005, IEEE Trans. Autom. Control..

[16]  Wei Ren,et al.  Stochastic adaptive prediction and model reference control , 1994, IEEE Trans. Autom. Control..