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Learning for control of dynamical systems with formal guarantees remains achallenging task. This paper proposes a learning framework to simultaneouslystabilize an unknown nonlinear system with a neural controller and learn aneural Lyapunov function to certify a region of attraction (ROA) for theclosed-loop system. The algorithmic structure consists of two neural networksand a satisfiability modulo theories (SMT) solver. The first neural network isresponsible for learning the unknown dynamics. The second neural network aimsto identify a valid Lyapunov function and a provably stabilizing nonlinearcontroller. The SMT solver then verifies that the candidate Lyapunov functionindeed satisfies the Lyapunov conditions. We provide theoretical guarantees ofthe proposed learning framework in terms of the closed-loop stability for theunknown nonlinear system. We illustrate the effectiveness of the approach witha set of numerical experiments.

Neural Lyapunov Control of Unknown Nonlinear Systems with Stability Guarantees