Neural learning of stable dynamical systems based on data-driven Lyapunov candidates

Nonlinear dynamical systems are a promising representation to learn complex robot movements. Besides their undoubted modeling power, it is of major importance that such systems work in a stable manner. We therefore present a neural learning scheme that estimates stable dynamical systems from demonstrations based on a two-stage process: first, a data-driven Lyapunov function candidate is estimated. Second, stability is incorporated by means of a novel method to respect local constraints in the neural learning. We show in two experiments that this method is capable of learning stable dynamics while simultaneously sustaining the accuracy of the estimate and robustly generates complex movements.