Robust data-driven state-feedback design

TL;DR

This paper introduces a data-driven method for designing robust state-feedback controllers for discrete-time LTI systems using only a single noisy data trajectory, eliminating the need for explicit model knowledge.

Contribution

It provides a novel data-driven characterization of uncertain closed-loop matrices and a controller design framework with stability and performance guarantees, including extensions with partial model knowledge.

Findings

Successfully designed controllers with stability guarantees from noisy data.

Framework encompasses $ ext{H}_ ext{infty}$ control as a special case.

Numerical example demonstrates effectiveness of the approach.

Abstract

We consider the problem of designing robust state-feedback controllers for discrete-time linear time-invariant systems, based directly on measured data. The proposed design procedures require no model knowledge, but only a single open-loop data trajectory, which may be affected by noise. First, a data-driven characterization of the uncertain class of closed-loop matrices under state-feedback is derived. By considering this parametrization in the robust control framework, we design data-driven state-feedback gains with guarantees on stability and performance, containing, e.g., the $\mathcal{H}_\infty$-control problem as a special case. Further, we show how the proposed framework can be extended to take partial model knowledge into account. The validity of the proposed approach is illustrated via a numerical example.