Non-Asymptotic Analysis of Robust Control from Coarse-Grained Identification

TL;DR

This paper analyzes the sample complexity needed for coarse system identification to achieve robust control, showing that simple models suffice and require fewer samples than precise identification, with guarantees on control performance.

Contribution

It provides non-asymptotic bounds on the number of samples needed for coarse model approximation that guarantees robust control performance, improving upon prior precise identification methods.

Findings

Simple models can achieve control objectives with fewer samples.

Bounds on sample complexity depend on system stability and input constraints.

Controllers designed on approximate models perform well on true systems.

Abstract

This work explores the trade-off between the number of samples required to accurately build models of dynamical systems and the degradation of performance in various control objectives due to a coarse approximation. In particular, we show that simple models can be easily fit from input/output data and are sufficient for achieving various control objectives. We derive bounds on the number of noisy input/output samples from a stable linear time-invariant system that are sufficient to guarantee that the corresponding finite impulse response approximation is close to the true system in the $\mathcal{H}_\infty$-norm. We demonstrate that these demands are lower than those derived in prior art which aimed to accurately identify dynamical models. We also explore how different physical input constraints, such as power constraints, affect the sample complexity. Finally, we show how our analysis fits within the established framework of robust control, by demonstrating how a controller designed for an approximate system provably meets performance objectives on the true system.