# Robust Online Control with Model Misspecification

arXiv: https://arxiv.org/abs/2107.07732 · HTML: https://mlsanity.com/paper/2107.07732/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 34 references that are in the map.
- First posted on arXiv 16 Jul 2021.

## Builds on (most cited first, 18 of 18)

- [Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification](https://mlsanity.com/paper/1802.08334/) (2018)
- [Online Control with Adversarial Disturbances](https://mlsanity.com/paper/1902.08721/) (2019)
- [Information Theoretic Regret Bounds for Online Nonlinear Control](https://mlsanity.com/paper/2006.12466/) (2020)
- [Near optimal finite time identification of arbitrary linear dynamical systems](https://mlsanity.com/paper/1812.01251/) (2018)
- [Improper Learning for Non-Stochastic Control](https://mlsanity.com/paper/2001.09254/) (2020)
- [Active Learning for Nonlinear System Identification with Guarantees](https://mlsanity.com/paper/2006.10277/) (2020)
- [Non-asymptotic Identification of LTI Systems from a Single Trajectory](https://mlsanity.com/paper/1806.05722/) (2018)
- [Learning Linear Dynamical Systems with Semi-Parametric Least Squares](https://mlsanity.com/paper/1902.00768/) (2019)
- [Online Linear Quadratic Control](https://mlsanity.com/paper/1806.07104/) (2018)
- [The Nonstochastic Control Problem](https://mlsanity.com/paper/1911.12178/) (2019)
- [Black-Box Control for Linear Dynamical Systems](https://mlsanity.com/paper/2007.06650/) (2020)
- [Regret Bounds for Adaptive Nonlinear Control](https://mlsanity.com/paper/2011.13101/) (2020)
- [Learning the Linear Quadratic Regulator from Nonlinear Observations](https://mlsanity.com/paper/2010.03799/) (2020)
- [No-Regret Prediction in Marginally Stable Systems](https://mlsanity.com/paper/2002.02064/) (2020)
- [Competitive Control with Delayed Imperfect Information](https://mlsanity.com/paper/2010.11637/) (2020)
- [A Regret Minimization Approach to Iterative Learning Control](https://mlsanity.com/paper/2102.13478/) (2021)
- [Finite Time Adaptive Stabilization of LQ Systems](https://mlsanity.com/paper/1807.09120/) (2018)
- [Adaptive Robust Model Predictive Control with Matched and Unmatched Uncertainty](https://mlsanity.com/paper/2104.08261/) (2021)

## Built on by (most cited first, 4 of 4)

- [Optimal Rates for Bandit Nonstochastic Control](https://mlsanity.com/paper/2305.15352/) (2023)
- [Online Nonstochastic Control with Adversarial and Static Constraints](https://mlsanity.com/paper/2302.02426/) (2023)
- [Regret Analysis of Multi-task Representation Learning for Linear-Quadratic Adaptive Control](https://mlsanity.com/paper/2407.05781/) (2024)
- [Optimizing the Preconditioner: A Black-box Online-to-Nonconvex Conversion with Static Regret Minimization Oracles](https://mlsanity.com/paper/2607.17607/) (2026)

## Abstract (arXiv)

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 ℓ2-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 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 ℓ2-gain whose dimension dependence is near optimal.