Identification of Box-Jenkins models using structured ARX models and nuclear norm relaxation*

In this contribution we present a method to estimate structured high order ARX models. By this we mean that the estimated model, despite its high order is close to a low order model. This is achieved by adding two terms to the least-squares cost function. These two terms correspond to nuclear norms of two Hankel matrices. These Hankel matrices are constructed from the impulse response coefficients of the inverse noise model, and the numerator polynomial of the model dynamics, respectively. In a simulation study the method is shown to be competitive as compared to the prediction error method. In particular, in the study the performance degrades more gracefully than for the Prediction Error Method when the signal to noise ratio decreases.