Data-Driven Estimation of Region of Attraction Using Koopman Operator and Reverse Trajectory

Abstract

We propose to estimate the region of attraction (ROA) for the stability of nonlinear systems from only system measurement data and without knowledge of the system model. The key to our result is the use of Koopman operator theory to approximate the nonlinear dynamics in linear coordinates. This approximation is typically more accurate than the traditional Jacobian-based linearization method. We then employ the Extended Dynamic Mode Decomposition (EDMD) method to estimate the linear approximation of the system through data. This is then used to construct a Lyapunov function that helps estimate the ROA. However, this estimate is typically very conservative. The trajectory reversing method is then used on the set of points that form this conservative estimate, to enlarge the ROA approximation. The output of EDMD is also utilized in the trajectory reversing method, keeping the entire analysis data-driven. Finally, an example is used to show the accuracy of this data-driven method, despite not knowing the system.