Data-driven stabilization of nonlinear systems via descriptor embedding

TL;DR

This paper presents a data-driven approach for stabilizing nonlinear systems using descriptor embedding, providing LMI conditions for controller design, and extending to uncertain and noisy data scenarios with region of attraction estimation.

Contribution

It introduces a novel descriptor embedding framework for nonlinear systems and develops data-dependent LMI conditions for stabilizing controller synthesis, including uncertainty and noise considerations.

Findings

LMI conditions successfully stabilize nonlinear systems from data.

Method extends to uncertain and noisy data scenarios.

Region of attraction can be estimated solely from data.

Abstract

We introduce the notion of descriptor embedding for nonlinear systems and use it for the data-driven design of stabilizing controllers. Specifically, we provide sufficient data-dependent LMI conditions which, if feasible, return a stabilizing nonlinear controller of the form $u=K(x)Z(x)$ where $K(x)$ belongs to a polytope and $Z$ is a user-defined function. The proposed method is then extended to account for the presence of uncertainties and noisy data. Furthermore, a method to estimate the resulting region of attraction is given using only data. Simulation examples are used to illustrate the results and compare them to existing methods from the literature.