Nuclear Norm Subspace Identification (N2SID) for short data batches

TL;DR

This paper introduces N2SID, a novel subspace identification method that leverages nuclear norm minimization and structural knowledge of data matrices to improve system identification from short data batches.

Contribution

The paper presents N2SID, a convex optimization-based subspace identification method that incorporates structural properties of data matrices, enhancing accuracy with limited data.

Findings

N2SID outperforms N4SID in short data batch scenarios.

N2SID effectively integrates structural knowledge into the identification process.

Numerical simulations demonstrate improved accuracy of N2SID.

Abstract

Subspace identification is revisited in the scope of nuclear norm minimization methods. It is shown that essential structural knowledge about the unknown data matrices in the data equation that relates Hankel matrices constructed from input and output data can be used in the first step of the numerical solution presented. The structural knowledge comprises the low rank property of a matrix that is the product of the extended observability matrix and the state sequence and the Toeplitz structure of the matrix of Markov parameters (of the system in innovation form). The new subspace identification method is referred to as the N2SID (twice the N of Nuclear Norm and SID for Subspace IDentification) method. In addition to include key structural knowledge in the solution it integrates the subspace calculation with minimization of a classical prediction error cost function. The nuclear norm relaxation enables us to perform such integration while preserving convexity. The advantages of N2SID are demonstrated in a numerical open- and closed-loop simulation study. Here a comparison is made with another widely used SID method, i.e. N4SID. The comparison focusses on the identification with short data batches, i.e. where the number of measurements is a small multiple of the system order.