Non-Asymptotic State-Space Identification of Closed-Loop Stochastic Linear Systems using Instrumental Variables

Abstract

The paper suggests a generalization of the Sign-Perturbed Sums (SPS) finite sample system identification method for the identification of closed-loop observable stochastic linear systems in state-space form. The solution builds on the theory of matrix-variate regression and instrumental variable methods to construct distribution-free confidence regions for the state-space matrices. Both direct and indirect identification are studied, and the exactness as well as the strong consistency of the construction are proved. Furthermore, a new, computationally efficient ellipsoidal outer-approximation algorithm for the confidence regions is proposed. The new construction results in a semidefinite optimization problem which has an order-of-magnitude smaller number of constraints, as if one applied the ellipsoidal outer-approximation after vectorization. The effectiveness of the approach is also demonstrated empirically via a series of numerical experiments.

arXiv comment12 pages, 4 tables, 3 figures

References in corpus (3)

• Sign-Perturbed Sums: A New System Identification Approach for Constructing Exact Non-Asymptotic Confidence Regions in Linear Regression Models
• Non-asymptotic Identification of Linear Dynamical Systems Using Multiple Trajectories
• Perturbed Datasets Methods for Hypothesis Testing and Structure of Corresponding Confidence Sets