Bibliographic Details
| Title: |
Data-driven control via Petersen's lemma |
| Authors: |
Bisoffi, Andrea, De Persis, Claudio, Tesi, Pietro |
| Publication Year: |
2021 |
| Collection: |
Computer Science
Mathematics |
| Subject Terms: |
Electrical Engineering and Systems Science - Systems and Control, Mathematics - Dynamical Systems, Mathematics - Optimization and Control |
| More Details: |
We address the problem of designing a stabilizing closed-loop control law directly from input and state measurements collected in an open-loop experiment. In the presence of noise in data, we have that a set of dynamics could have generated the collected data and we need the designed controller to stabilize such set of data-consistent dynamics robustly. For this problem of data-driven control with noisy data, we advocate the use of a popular tool from robust control, Petersen's lemma. In the cases of data generated by linear and polynomial systems, we conveniently express the uncertainty captured in the set of data-consistent dynamics through a matrix ellipsoid, and we show that a specific form of this matrix ellipsoid makes it possible to apply Petersen's lemma to all of the mentioned cases. In this way, we obtain necessary and sufficient conditions for data-driven stabilization of linear systems through a linear matrix inequality. The matrix ellipsoid representation enables insights and interpretations of the designed control laws. In the same way, we also obtain sufficient conditions for data-driven stabilization of polynomial systems through (convex) sum-of-squares programs. The findings are illustrated numerically. |
| Document Type: |
Working Paper |
| DOI: |
10.1016/j.automatica.2022.110537 |
| Access URL: |
http://arxiv.org/abs/2109.12175 |
| Accession Number: |
edsarx.2109.12175 |
| Database: |
arXiv |
