Non-Asymptotic Bounds for Closed-Loop Identification of Unstable Nonlinear Stochastic Systems
This addresses a theoretical gap for control theorists working with unstable systems, though it appears incremental as it extends existing bounded-error frameworks to more challenging scenarios.
The paper tackles parameter estimation for unstable nonlinear stochastic systems in closed-loop settings, establishing non-asymptotic error bounds that apply when state trajectories remain in informative regions, with examples showing utility where prior methods fail.
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.