Augmented Neural Lyapunov Control

Machine learning-based techniques have recently been adapted to solve control problems. The Neural Lyapunov Control (NLC) method is one such example. This approch combines Artificial Networks with Satisfiability Modulo Theories (SMT) solvers synthesise stabilising laws and prove their formal correctness. formers are trained over a dataset of state-space samples generate candidate functions, whilst the SMT tasked certifying correctness continuous domain or returning counterexample. Despite approach attractiveness, issues can occur due subsequent calls module oftentimes similar counterexamples, turning out be uninformative leading overfitting. Additionally, network weights usually initialised pre-computed gains from state-feedback controllers, e.g. Linear-Quadratic Regulators. initialisation requires user time expertise. In this work, we present an Augmented NLC that alleviates these drawbacks, removes need for further improves counterexample generation. As result, allows nonlinear (as well as linear) requiring solely knowledge system dynamics. proposed tested challenging benchmarks Lorenz attractor, outperforming existing in terms successful synthesis rate. developed framework released open-source at https://released upon acceptance.