Physics

Nonlinear system

Mathematics

Agronomy

Biology

Algorithm

Mathematical optimization

Quadratic equation

Artificial intelligence

Controller (irrigation)

Control (management)

Full state feedback

Class (philosophy)

Geometry

Computer science

Quantum mechanics

Control theory (sociology)

State (computer science)

Systems & Control Letters

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.

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