LEARNING RELIABLE ADAPTIVE REGION-OFATTRACTION REPRESENTATIONS FOR NONLINEAR DYNAMICAL SYSTEMS

Learning regions of attraction (RoAs) of nonlinear dynamical systems remains challenging because existing approaches often rely on a single global representation, creating a tradeoff between expressiveness, constructability, and scalability. Moreover, many practically relevant controllers are designed or learned primarily for control performance rather than jointly with an RoA certificate, motivating post-training RoA analysis without modifying the given controller. We propose a hybrid framework that learns and represents the RoA through complementary local components. A quadratic Lyapunov representation derived from closed-loop linearization is refined under the nonlinear dynamics to obtain a trusted local core. Starting from this core, the framework learns convergent states, lifts them into continuous regions through locally validated geometric representations, and augments residual regions using flow-informed patches. The resulting hybrid representation is independently evaluated through finite-sample boundedness and reach-to-core validation, providing explicit statistical reliability without requiring the RoA to conform to a single global certificate. The framework applies to fixed closed-loop nonlinear systems, requires no controller retraining or certificate-aware controller synthesis, and is independent of the controller representation. Experiments on CartPole and six-dimensional quadrotor systems demonstrate substantial expansion beyond the trusted local core while establishing 99.9% reliability at 99.9% confidence.