Learning Stable and Passive Neural Differential Equations

TL;DR

This paper introduces a new class of neural differential equations that are inherently stable and passive by design, leveraging Lyapunov functions and Hamiltonian structures to ensure robust dynamics.

Contribution

It proposes a novel neural differential equation framework that guarantees stability and passivity using Lyapunov functions and Hamiltonian-like structures, enhancing robustness.

Findings

Effective on damped double pendulum system

Models exhibit intrinsic stability and passivity

Demonstrates robustness of the proposed approach

Abstract

In this paper, we introduce a novel class of neural differential equation, which are intrinsically Lyapunov stable, exponentially stable or passive. We take a recently proposed Polyak Lojasiewicz network (PLNet) as an Lyapunov function and then parameterize the vector field as the descent directions of the Lyapunov function. The resulting models have a same structure as the general Hamiltonian dynamics, where the Hamiltonian is lower- and upper-bounded by quadratic functions. Moreover, it is also positive definite w.r.t. either a known or learnable equilibrium. We illustrate the effectiveness of the proposed model on a damped double pendulum system.