Trade-offs in learning controllers from noisy data

TL;DR

This paper introduces a new approach for designing stabilizing controllers from noisy data in linear systems, using instantaneous disturbance bounds, which reduces conservativeness compared to energy-based models.

Contribution

The work proposes a convex programming method that directly handles instantaneous disturbance bounds, improving controller design efficiency and data consistency analysis.

Findings

Convex program yields larger feasible sets for controller design.

System matrices consistent with data decrease as data size increases.

Numerical examples demonstrate the effectiveness of the approach.

Abstract

In data-driven control, a central question is how to handle noisy data. In this work, we consider the problem of designing a stabilizing controller for an unknown linear system using only a finite set of noisy data collected from the system. For this problem, many recent works have considered a disturbance model based on energy-type bounds. Here, we consider an alternative more natural model where the disturbance obeys instantaneous bounds. In this case, the existing approaches, which would convert instantaneous bounds into energy-type bounds, can be overly conservative. In contrast, without any conversion step, simple arguments based on the S-procedure lead to a very effective controller design through a convex program. Specifically, the feasible set of the latter design problem is always larger, and the set of system matrices consistent with data is always smaller and decreases significantly with the number of data points. These findings and some computational aspects are examined in a number of numerical examples.