Automated and optimal system identification by canonical variables

The completely automatic, reliable and optimal identification of linear dynamical systems has the potential to revolutionize the operation of control systems, signal processing, and system monitoring. In this paper, the theory, methods, and results of such an identification procedure are outlined. The procedure applies to a general multivariable, time-invariant linear system with stochastic disturbances that may be nonstationary and the system may be unstable and have feedback. Deterministic polynomial time functions may be present in the observations. The computation involves primarily the singular value decomposition (SVD). The model state order is automatically determined using an optimal statistical order selection procedure, a small sample version of the Akaike information criterion (AIC). A multivariable stochastic state space model of the input-output dynamics and system disturbances is computed by multivariate regression. The identified model accuracy is described by confidence bands on the transfer function and power spectrum as well as maximum singular value quantities. These can be used directly in robust control design.

[1]  Michel Gevers,et al.  On the problem of structure selection for the identification of stationary stochastic processes , 1982 .

[2]  A. Lindquist,et al.  Markovian representation of discrete-time stationary stochastic vector processes , 1981, 1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[3]  H. Akaike,et al.  Information Theory and an Extension of the Maximum Likelihood Principle , 1973 .

[4]  C. Loan.  Generalizing the Singular Value Decomposition , 1976 .

[5]  J. Baillieul,et al.  Identification and filtering of nonlinear systems using canonical variate analysis , 1990, 29th IEEE Conference on Decision and Control.

[6]  Solomon Kullback,et al.  Information Theory and Statistics , 1960 .

[7]  Wallace E. Larimore.  Accuracy Confidence Bands Including The Bias Of Model Under-Fitting , 1993, 1993 American Control Conference.

[8]  Jim V. Candy,et al.  Invariant system description of the stochastic realization , 1979, Autom..

[9]  H. Akaike.  Canonical Correlation Analysis of Time Series and the Use of an Information Criterion , 1976 .

[10]  Robert H. Shumway,et al.  Improved estimators of Kullback-Leibler information for autoregressive model selection in small samples , 1990 .

[11]  H. Hotelling.  Relations Between Two Sets of Variates , 1936 .

[12]  Clifford M. Hurvich,et al.  Bias of the corrected AIC criterion for underfitted regression and time series models , 1991 .

[13]  H. Akaike.  Markovian Representation of Stochastic Processes by Canonical Variables , 1975 .

[14]  Wallace E. Larimore,et al.  Canonical variate analysis in identification, filtering, and adaptive control , 1990, 29th IEEE Conference on Decision and Control.

[15]  Wallace E. Larimore,et al.  Predictive inference, sufficiency, entropy and an asymptotic likelihood principle , 1983 .

[16]  Clifford M. Hurvich,et al.  Regression and time series model selection in small samples , 1989 .

[17]  R. L. Haller,et al.  Online adaptive control of unstable aircraft wing flutter , 1990, 29th IEEE Conference on Decision and Control.