《《On consistency of closed-loop subspace identification with innovation estimation》.pdfVIP

43rd IEEE Conference on Decision and Control WeB11.2 December 14-17, 2004 Atlantis, Paradise Island, Bahamas On Consistency of Closed-loop Subspace Identification with Innovation Estimation Weilu Lin, S. Joe Qin*, and Lennart Ljung Abstract— In this paper, we show that the consistency of exhibit the first drawback and propose parsimonious SIMs closed-loop subspace identification methods (SIMs) can be (PARSIMs) for open-loop applications. achieved through innovation estimation. Based on this analysis, Contrary to the open loop SIMs, the traditional SIMs a sufficient condition for the consistency of a new proposed closed-loop SIM is given. A consistent estimate of the Kalman (e.g., CVA, N4SID and MOESP) are biased under closed- gain under closed-loop conditions is also provided based on loop condition. Verhaegen [10] proposed a closed-loop the algorithm. A multi-input-multi-output (MIMO) simulation SIM via the identification of an overall open-loop state shows that it is consistent under closed-loop condition, when space model followed by a model reduction step to obtain traditional SIMs fail to provide consistent estimates. state space representations of the plant and controller. The disadvantages of the approach is that a high order overall I. INTRODUCTION system has to be identified, which introduces extra compu- The closed-loop i