The Lyapunov Neural Network: Adaptive Stability Certification for Safe Learning of Dynamical Systems

TL;DR

This paper introduces a neural network-based Lyapunov function that certifies safety regions in nonlinear dynamical systems, enabling safe learning and control without requiring explicit system models.

Contribution

It presents a novel adaptive training algorithm for neural Lyapunov functions that accurately certifies safety regions solely from input-output data.

Findings

Successfully learned the safe region for a simulated inverted pendulum.

Demonstrated potential for integration with safe learning algorithms.

Applicable to nonlinear systems without explicit model knowledge.

Abstract

Learning algorithms have shown considerable prowess in simulation by allowing robots to adapt to uncertain environments and improve their performance. However, such algorithms are rarely used in practice on safety-critical systems, since the learned policy typically does not yield any safety guarantees. That is, the required exploration may cause physical harm to the robot or its environment. In this paper, we present a method to learn accurate safety certificates for nonlinear, closed-loop dynamical systems. Specifically, we construct a neural network Lyapunov function and a training algorithm that adapts it to the shape of the largest safe region in the state space. The algorithm relies only on knowledge of inputs and outputs of the dynamics, rather than on any specific model structure. We demonstrate our method by learning the safe region of attraction for a simulated inverted pendulum. Furthermore, we discuss how our method can be used in safe learning algorithms together with statistical models of dynamical systems.