Gray-Box Parsimonious Subspace Identification of Hammerstein-Type Systems

In this article, a gray-box parsimonious subspace identification method using sampled dynamical and steady-state data is proposed for block-oriented Hammerstein-type systems. Compared with the conventional subspace identification methods based on over-parameterized models, the proposed method assumes parsimonious models, where the number of parameters is as minimal as possible to ensure the model accuracy, especially for highly nonlinear models. Generally, the available dynamical data do not contain adequate information on the low-frequency characteristics of the system. To improve the accuracy of model identification, the steady-state information of the system is taken into account, and a multiregularization method is developed, where the whole model parameters are estimated in a hierarchical, iterative manner from two sets of data: the dynamical input-output data and the steady-state input-output data. The use of parsimonious models and hierarchical estimation can significantly reduce the size of the associated parameter estimation error covariance matrix, thus improving the model accuracy and decreasing the variance of the estimated parameters, compared with the over-parametrization methods only using dynamical data. The effectiveness and merits are demonstrated by a simulation example and a real-world example.