Least-squares identification of closed-loop systems

Abstract

The problem of least-squares estimation of closed-loop systems is examined. The particular configuration considered is the single input-single output discrete linear system controlled by a linear, stationary feedback regulator. Results are obtained which determine the conditions for uniqueness and consistency of the least-squares estimates of the forward-path transfer function. In particular, it is shown that if two orthogonal unobservable noise sources are present, one in each path, the system is uniquely identifiable. When the feedback path is noise-free the uniqueness of the estimates is dependent upon the order of the regulator regression polynomials. The consistency of the estimates in the case of a white forward-path disturbance is assured provided that there is at least one delay term in the loop.