Non-Asymptotic Bounds for Closed-Loop Identification of Unstable Nonlinear Stochastic Systems

TL;DR

This paper derives non-asymptotic bounds for least squares estimation in unstable nonlinear stochastic systems, providing guarantees on estimation error during informative state regions, which is novel for such challenging systems.

Contribution

It introduces non-asymptotic error bounds for closed-loop system identification in unstable nonlinear stochastic systems, a significant advancement over existing asymptotic results.

Findings

Non-asymptotic error bounds are established for certain unstable systems.

Guarantees hold with high probability during informative state regions.

Results are applicable even when the entire state space is informative.

Abstract

We consider the problem of least squares parameter estimation from single-trajectory data for discrete-time, unstable, closed-loop nonlinear stochastic systems, with linearly parameterised uncertainty. Assuming a region of the state space produces informative data, and the system is sub-exponentially unstable, we establish non-asymptotic guarantees on the estimation error at times where the state trajectory evolves in this region. If the whole state space is informative, high probability guarantees on the error hold for all times. Examples are provided where our results are useful for analysis, but existing results are not.