Automated and Objective System Identification Based on Canonical Variables

The completely automatic, reliable and objective 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 such as a bias, trend, quadratic, etc., may be present in the observations. The computation involves primarily the singular value decomposition (SVD) which is always numerically accurate and stable, and no iterative parameter optimization is involved. 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. The identification procedure is completely automated - essentially data is input and a state space model is output of the statistically significant process dynamics and disturbance characteristics. The procedure is available in the ADAPTX software package which has been applied to a wide range of aerospace, process control, and industrial problems.