N2SID: Nuclear Norm Subspace Identification

TL;DR

N2SID introduces a convex nuclear norm optimization approach for subspace identification of multivariable state space models, improving accuracy and flexibility by avoiding instrumental variables and enabling constraint inclusion.

Contribution

The paper presents a novel nuclear norm-based convex optimization method for subspace identification that incorporates constraints and eliminates the need for instrumental variables.

Findings

Improved accuracy in model prediction for short data sequences.

Efficient ADMM implementation for the proposed method.

Validation on real data from the DaSIy library.

Abstract

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.