On data-driven stabilization of systems with nonlinearities satisfying quadratic constraints

In this paper, we directly design a state feedback controller that stabilizes a class of uncertain nonlinear systems solely based on input-state data collected from a finite-length experiment. Necessary and sufficient conditions are derived to guarantee that the system is absolutely stabilizable and a controller is designed. Results derived under some relaxed prior information about the system, strengthened data assumptions and perturbed data are also discussed. All the results are based on semi-definite programs that depend on input-state data only, which - once solved - directly return controllers. As such they represent end-to-end solutions to the problem of learning control from data for an important class of nonlinear systems. Numerical examples illustrate the method with different levels of prior information. (c) 2022 The Author(s). Published by Elsevier B.V.This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).