Nuclear norm subspace identification method for Hammerstein system identification

In this paper, in order to solve the dimension problem in over-parameterized method (OPM) and the rank constraint problem in subspace identification method (SIM), The nuclear norm subspace identification method (N2SID) is proposed with a combination of nuclear norm minimization (NNM) and least-parameterized method (LPM). NNM is a heuristic convex relaxation of the rank minimization, and preprocesses the measured data to obtain an optimized Hankel matrix with lower rank for subspace identification. In addition, NNM descends the nonzero singular values of Hankel matrix caused by extra noise near to zero to improve the order identification of SIM. LPM takes into account the dimension problem in the conventional OPM and identifies the Hammerstein system with the least estimation parameters. N2SID benefits the advantages of both NNM and LPM to improve the identification of Hammerstein system. Furthermore, a numerical example is presented to illustrate the improvement on Hammerstein system identification by N2SID through comparing with LPM and OPM.