Closed-loop subspace identification of Hammerstein-Wiener models

In this paper we present a novel algorithm to identify MIMO Hammerstein-Wiener systems under open and closed-loop conditions.We reformulate a linear regression problem, commonly used as the first step in closed loop subspace identification, as an intersection problem which can be solved by using canonical correlation analysis (CCA). This makes it possible to utilize ideas from machine learning to estimate the static nonlinearities of Hammerstein-Wiener systems, using kernel canonical correlation analysis (KCCA). In the second step the state sequence is estimated and consequently the dynamic part can be identified. The effectiveness of the approach is illustrated with a closed-loop simulation example.