Neural Lyapunov Control of Unknown Nonlinear Systems with Stability Guarantees
This addresses the challenge of ensuring stability in control systems for applications like robotics or autonomous vehicles, though it is incremental as it builds on existing neural and Lyapunov methods.
The paper tackled the problem of stabilizing unknown nonlinear dynamical systems with formal guarantees by proposing a learning framework that uses neural networks to learn a controller and a Lyapunov function, with verification via an SMT solver, achieving closed-loop stability as demonstrated in numerical experiments.
Learning for control of dynamical systems with formal guarantees remains a challenging task. This paper proposes a learning framework to simultaneously stabilize an unknown nonlinear system with a neural controller and learn a neural Lyapunov function to certify a region of attraction (ROA) for the closed-loop system. The algorithmic structure consists of two neural networks and a satisfiability modulo theories (SMT) solver. The first neural network is responsible for learning the unknown dynamics. The second neural network aims to identify a valid Lyapunov function and a provably stabilizing nonlinear controller. The SMT solver then verifies that the candidate Lyapunov function indeed satisfies the Lyapunov conditions. We provide theoretical guarantees of the proposed learning framework in terms of the closed-loop stability for the unknown nonlinear system. We illustrate the effectiveness of the approach with a set of numerical experiments.