From Noisy Data to Feedback Controllers: Nonconservative Design via a Matrix S-Lemma

• Published in: IEEE transactions on automatic control Vol. 67; no. 1; pp. 162 - 175
• Main Authors: van Waarde, Henk J., Camlibel, M. Kanat, Mesbahi, Mehran
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.01.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Control design; Control systems; Covariance matrices; Data-driven control; Feedback control; Independent variables; Linear matrix inequalities; LMIs; Mathematical analysis; Noise measurement; Optimal control; Predictive control; robust control; Tuning; uncertain systems

In this article, we propose a new method to obtain feedback controllers of an unknown dynamical system directly from noisy input/state data. The key ingredient of our design is a new matrix S-lemma that will be proven in this article. We provide both strict and nonstrict versions of this S-lemma, wh...