Robust Online Control with Model Misspecification

Xinyi Chen, Udaya Ghai, Elad Hazan, Alexandre Megretski

Research output: Contribution to journalConference articlepeer-review

1 Scopus citations


We study online control of an unknown nonlinear dynamical system that is approximated by a time-invariant linear system with model misspecification. Our study focuses on robustness, a measure of how much deviation from the assumed linear approximation can be tolerated by a controller while maintaining finite `2-gain. A basic methodology to analyze robustness is via the small gain theorem. However, as an implication of recent lower bounds on adaptive control, this method can only yield robustness that is exponentially small in the dimension of the system and its parametric uncertainty. The work of Cusumano and Poolla (1988a) shows that much better robustness can be obtained, but the control algorithm is inefficient, taking exponential time in the worst case. In this paper we investigate whether there exists an efficient algorithm with provable robustness beyond the small gain theorem. We demonstrate that for a fully actuated system, this is indeed attainable. We give an efficient controller that can tolerate robustness that is polynomial in the dimension and independent of the parametric uncertainty; furthermore, the controller obtains an `2-gain whose dimension dependence is near optimal.

Original languageEnglish (US)
Pages (from-to)1163-1175
Number of pages13
JournalProceedings of Machine Learning Research
StatePublished - 2022
Externally publishedYes
Event4th Annual Learning for Dynamics and Control Conference, L4DC 2022 - Stanford, United States
Duration: Jun 23 2022Jun 24 2022

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability


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