Data-Driven Stabilization of Nonlinear Systems via Taylor’s Expansion

Lyapunov’s indirect methodLyapunovindirect method is one of the oldest and most popular approaches to model-based controller design for nonlinear systemsNonlinearsystem. When the explicit model of the nonlinear systemNonlinearsystem is unavailable for designing such a linear controller, finite-length off-line data is used to obtain a data-based representation of the closed-loop system, and a data-driven linear control law is designed to render the considered equilibrium locally asymptotically stable. This work presents a systematic approach for data-driven linear stabilizer design for continuous-time and discrete-time general nonlinear systemsNonlinearsystem. Moreover, under mild conditions on the nonlinear dynamics, we show that the region of attractionRegion of attraction of the resulting locally asymptotically stable closed-loop system can be estimated using data.