Data-Driven Approach for Uncertainty Propagation and Reachability Analysis in Dynamical Systems
arXiv:2001.07668
Abstract
In this paper, we propose a data-driven approach for uncertainty propagation and reachability analysis in a dynamical system. The proposed approach relies on the linear lifting of a nonlinear system using linear Perron-Frobenius (P-F) and Koopman operators. The uncertainty can be characterized in terms of the moments of a probability density function. We demonstrate how the P-F and Koopman operators are used for propagating the moments. Time-series data is used for the finite-dimensional approximation of the linear operators, thereby enabling data-driven approach for moment propagation. Simulation results are presented to demonstrate the effectiveness of the proposed method.
Accepted in the 2020 American Control Conference, to be held in Denver, CO, USA on July 1-3, 2020