Non-asymptotic System Identification for Linear Systems with Nonlinear Policies

Yingying Li, Tianpeng Zhang, Subhro Das, Jeff Shamma, Na Li

Research output: Chapter in Book/Report/Conference proceedingConference contribution


This paper considers a single-trajectory system identification problem for linear systems under general nonlinear and/or time-varying policies with i.i.d. random excitation noises. The problem is motivated by safe learning-based control for constrained linear systems, where the safe policies during the learning process are usually nonlinear and time-varying for satisfying the state and input constraints. In this paper, we provide a non-asymptotic error bound for least square estimation when the data trajectory is generated by any nonlinear and/or time-varying policies as long as the generated state and action trajectories are bounded. This significantly generalizes the existing non-asymptotic guarantees for linear system identification, which usually consider i.i.d. random inputs or linear policies. Interestingly, our error bound is consistent with that for linear policies with respect to the dependence on the trajectory length, system dimensions, and excitation levels. Lastly, we demonstrate the applications of our results by safe learning with robust model predictive control and provide numerical analysis.

Original languageEnglish (US)
Title of host publicationIFAC-PapersOnLine
EditorsHideaki Ishii, Yoshio Ebihara, Jun-ichi Imura, Masaki Yamakita
PublisherElsevier B.V.
Number of pages8
ISBN (Electronic)9781713872344
StatePublished - Jul 1 2023
Event22nd IFAC World Congress - Yokohama, Japan
Duration: Jul 9 2023Jul 14 2023

Publication series

ISSN (Electronic)2405-8963


Conference22nd IFAC World Congress


  • Identification for control
  • Learning for control
  • Stochastic system identification

ASJC Scopus subject areas

  • Control and Systems Engineering


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