Stable State Space SubSpace (S$^5$) Identification

TL;DR

This paper introduces a new, computationally efficient, closed-form state space subspace identification algorithm that guarantees stability without tuning parameters and is scalable to high-dimensional systems.

Contribution

The paper presents a novel stability-guaranteed subspace identification algorithm that is simple, tuning-free, and scalable, with proven consistency.

Findings

Algorithm is closed-form and tuning-free.

Scales efficiently to high-dimensional systems.

Proven to be consistent under reasonable conditions.

Abstract

State space subspace algorithms for input-output systems have been widely applied but also have a reasonably well-developedasymptotic theory dealing with consistency. However, guaranteeing the stability of the estimated system matrix is a major issue. Existing stability-guaranteed algorithms are computationally expensive, require several tuning parameters, and scale badly to high state dimensions. Here, we develop a new algorithm that is closed-form and requires no tuning parameters. It is thus computationally cheap and scales easily to high state dimensions. We also prove its consistency under reasonable conditions.