Data-Driven Quadratic Stabilization of Continuous LTI Systems. Issue 2 (2020)

• Record Type: Journal Article
• Authors: Dai, Tianyu; Sznaier, Mario; Solvas, Biel Roig
• Is Part Of: IFAC-PapersOnLine. Volume 53:Issue 2(2020)
• Page Start: 3965
• Page End: 3970
• Publication Date: 2020
• Subjects: Data-Driven Control -- Robust Control -- Quadratic Stability -- Semi-Definite Programming; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2020.12.2252
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: This paper introduces a simple data-driven quadratic stabilization control (DDQSC) method to design a state feedback controller based solely on experimental measurements while avoiding explicitly identifying the plant. Rather, we seek a controller guaranteed to quadratically stabilize all plants that could have possibly generated the observed data. While in principle this leads to a very challenging non-convex robust optimization problem, our main result provides a convex, albeit infinite-dimensional, necessary and sufficient condition for the existence of such a controller and its associated Lyapunov function. In the second part of the paper, we provide a tractable finite-dimensional convex relaxation of this condition and illustrate its effectiveness with several examples.