N2SID: Nuclear Norm Subspace Identification

The identification of multivariable state space models in innovation form is solved in a subspace identification framework using convex nuclear norm optimization. The convex optimization approach allows to include constraints on the unknown matrices in the data-equation characterizing subspace identification methods, such as the lower triangular block-Toeplitz of weighting matrices constructed from the Markov parameters of the unknown observer. The classical use of instrumental variables to remove the influence of the innovation term on the data equation in subspace identification is avoided. The avoidance of the instrumental variable projection step has the potential to improve the accuracy of the estimated model predictions, especially for short data length sequences. This is illustrated using a data set from the DaSIy library. An efficient implementation in the framework of the Alternating Direction Method of Multipliers (ADMM) is presented that is used in the validation study.