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

• 成果类型: Article
• 署名作者: Furieri, Luca; Guo, Baiwei; Martin, Andrea; Ferrari-Trecate, Giancarlo
• 署名单位: Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3180692
• 发表日期: 2023
• 页码: 2699-2714
• 关键词: safety; Noise measurement; Behavioral sciences; trajectory; Biological system modeling; Numerical models; data models; Data-driven control; learning-based control; Linear systems; optimal control; Robust control

摘要

As we transition toward 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.