Learning a Stable Dynamic System with a Lyapunov Energy Function for Demonstratives Using Neural Networks

TL;DR

This paper presents a neural network-based dynamic system algorithm that learns from demonstrations, extracting a Lyapunov energy function to ensure stability while maintaining high accuracy, validated on datasets and robotic experiments.

Contribution

Introduces a neural network algorithm that simultaneously learns a Lyapunov energy function and achieves stable, accurate dynamic system modeling from demonstration data.

Findings

Effective stability preservation demonstrated on LASA dataset

Successful robotic experiment validation

Neural network effectively learns Lyapunov function

Abstract

Autonomous Dynamic System (DS)-based algorithms hold a pivotal and foundational role in the field of Learning from Demonstration (LfD). Nevertheless, they confront the formidable challenge of striking a delicate balance between achieving precision in learning and ensuring the overall stability of the system. In response to this substantial challenge, this paper introduces a novel DS algorithm rooted in neural network technology. This algorithm not only possesses the capability to extract critical insights from demonstration data but also demonstrates the capacity to learn a candidate Lyapunov energy function that is consistent with the provided data. The model presented in this paper employs a straightforward neural network architecture that excels in fulfilling a dual objective: optimizing accuracy while simultaneously preserving global stability. To comprehensively evaluate the effectiveness of the proposed algorithm, rigorous assessments are conducted using the LASA dataset, further reinforced by empirical validation through a robotic experiment.