Data-driven control via Petersen's lemma. (November 2022)

• Record Type: Journal Article
• Authors: Bisoffi, Andrea; De Persis, Claudio; Tesi, Pietro
• Is Part Of: Automatica. Volume 145(2022)
• Publication Date: 2022-11
• Subjects: Data-based control -- Optimization-based controller synthesis -- Analysis of systems with uncertainty -- Robust control of nonlinear systems -- Linear matrix inequalities -- Sum-of-squares; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2022.110537
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: We address the problem of designing a stabilizing closed-loop control law directly from input and state measurements collected in an experiment. In the presence of a process disturbance 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 alternate (convex) sum-of-squares programs. The findings are illustrated numerically.