Non-Asymptotic Bounds for Closed-Loop Identification of Sub-Exponentially Growing Nonlinear Stochastic Systems

Abstract:We investigate the problem of least squares parameter estimation from single-trajectory data for discrete-time, unstable, closed-loop nonlinear stochastic systems. Specifically, we consider nonlinear systems with linearly parametrised uncertainty and additive i.i.d. process noise, in feedback with a control policy that is intentionally perturbed by an exploratory input. Assuming the open-loop dynamics satisfy a particular sub-exponential input-to-state growth property, and a region of the state space produces informative data, we establish non-asymptotic guarantees on the estimation error at times when 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 beyond existing works.

Systems and Control (eess.SY); Machine Learning (cs.LG); Optimization and Control (math.OC)

arXiv:2412.04157 [eess.SY]

(or arXiv:2412.04157v2 [eess.SY] for this version)

https://doi.org/10.48550/arXiv.2412.04157 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.