Subspace System Identification via Weighted Nuclear Norm Optimization

TL;DR

This paper introduces a weighted nuclear norm optimization approach for subspace system identification, improving model fit and reducing computational complexity through an efficient ADMM-based implementation.

Contribution

It proposes a novel weighted nuclear norm method for subspace identification that enhances fit and computational efficiency compared to existing techniques.

Findings

Improved fit on validation data.

Reduced size of optimization problems.

Effective use of ADMM for implementation.

Abstract

We present a subspace system identification method based on weighted nuclear norm approximation. The weight matrices used in the nuclear norm minimization are the same weights as used in standard subspace identification methods. We show that the inclusion of the weights improves the performance in terms of fit on validation data. As a second benefit, the weights reduce the size of the optimization problems that need to be solved. Experimental results from randomly generated examples as well as from the Daisy benchmark collection are reported. The key to an efficient implementation is the use of the alternating direction method of multipliers to solve the optimization problem.