A technique to design controllers for nonlinear systems from data consists of letting the controllers learn the nonlinearities, cancel them out and stabilize the closed-loop dynamics. When control and nonlinearities are unmatched, the technique leads to an approximate cancellation and local stability results are obtained. In this paper, we show that, if the system has some structure that the designer can exploit, an iterative use of the data leads to a globally stabilizing controller even when control and nonlinearities are unmatched.@en

We consider data-driven control of input-affine systems via approximate nonlinearity cancellation. Data-dependent semi-definite program is developed to characterize the stabilizer such that the linear dynamics of the closed-loop systems is stabilized and the influence of the nonlinear dynamics is decreased. Because of the additional nonlinearity brought by the state-dependent input vector field, nonlinearity cancellation is more difficult to achieve. We show that under some assumptions on the nonlinearity, the nonlinearity cancellation control approach can render the equilibrium locally asymptotically stable even if the additional nonlinearity is neglected. Data-based estimation of the region of the attraction is also presented.@en

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.@en