Near-Optimal Design of Safe Output Feedback Controllers from Noisy Data

TL;DR

This paper develops a data-driven control design method for safe, noisy systems, providing guarantees on safety and near-optimality that are robust to model uncertainty and applicable with various estimators.

Contribution

It introduces a quasiconvex relaxation approach for designing safe output feedback controllers from noisy data, ensuring near-optimality under small model mismatch.

Findings

Controller guarantees safety under bounded noise.

Suboptimality gap scales linearly with model mismatch.

Method is compatible with advanced behavioral estimators.

Abstract

As we transition towards the deployment of data-driven controllers for black-box cyberphysical systems, complying with hard safety constraints becomes a primary concern. Two key aspects should be addressed when input-output data are corrupted by noise: how much uncertainty can one tolerate without compromising safety, and to what extent is the control performance affected? By focusing on finite-horizon constrained linear-quadratic problems, we provide an answer to these questions in terms of the model mismatch incurred during a preliminary identification phase. We propose a control design procedure based on a quasiconvex relaxation of the original robust problem and we prove that, if the uncertainty is sufficiently small, the synthesized controller is safe and near-optimal, in the sense that the suboptimality gap increases linearly with the model mismatch level. Since the proposed method is independent of the specific identification procedure, our analysis holds in combination with state-of-the-art behavioral estimators beyond standard least-squares. The main theoretical results are validated by numerical experiments.