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.