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.