Finite-Sample Guarantees for State-Space System Identification Under Full State Measurements

Complementing data-driven models of dynamic systems with certificates of reliability and safety is of critical importance in many applications, such as in the design of robust control policies for unknown or uncertain systems. In this paper, we propose an efficient method to construct finite-sample confidence regions for the parameters of unknown linear systems in state-space form. The proposed procedure builds on the Sign-Perturbed Sums (SPS) paradigm and returns regions that are provably exact, i.e., contain the true parameters with the desired probability, using finite data and under minimal assumptions on the noise distribution. In particular, the noise distribution is only required to be symmetric about the origin, thus encompassing as special cases commonly studied noise settings, such as zero-mean Gaussian or Laplacian noise. The performance of our procedure is tested across different noise scenarios and compared to that of alternative approaches.