Subspace-based Identification Algorithms for Hammerstein and Wiener Models

Subspace-based algorithms for the simultaneous identification of the linear and nonlinear parts of multivariable Hammerstein and Wiener models are presented in this paper. The proposed algorithms consist basically of two steps. The first one is a standard subspace-based identification algorithm applied to an auxiliary multivariable linear system whose inputs (respectively outputs) are filtered versions of the original inputs (respectively outputs). The filters are the nonlinear functions describing the static nonlinearities for the Hammerstein case and its inverses for the Wiener case. The second step consists of a 2-norm minimization problem which is solved via Singular Value Decomposition. Consistency of the estimates can be guaranteed under weak assumptions. The performance of the proposed identification algorithms is illustrated through simulation examples.