Data-Efficient Learning-Based Estimation of Region of Attractions for Nonlinear Dynamic Systems

Estimation of the region of attraction (RoA) of dynamic systems is a challenging task due to complex nonlinear behaviors. Analytical approaches require accurate dynamic models and are commonly conservative. In this paper, we present a data-efficient, machine learning-based RoA estimation strategy for an unknown dynamic system with multiple attractors. Our approach constructs and maps the dynamics onto the Riemannian manifold with potential function. The initial RoA is estimated based on regions with low potential values and high gradient magnitudes. To refine the RoA boundaries, further sampling is directed towards regions adjacent to the initial estimation, ensuring an adaptive and efficient data collection process. A Morse graph-based RoA expansion strategy is finally applied to identify the boundaries of RoA. We demonstrate the proposed RoA estimation method by using both simulation and experimental results for inverted pendulums with various controllers. Comparison with other RoA estimation methods is also presented to demonstrate the superior data efficiency and accuracy of the proposed approach.