Learning Stable and Passive Neural Differential Equations

Jing Cheng; Ruigang Wang; Ian R. Manchester

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arXiv · 2404.12554

Learning Stable and Passive Neural Differential Equations

Jing Cheng·Ruigang Wang·Ian R. Manchester

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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.

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Jing Cheng, Ruigang Wang, Ian R. Manchester. 2024-04-19. Learning Stable and Passive Neural Differential Equations. https://arxiv.org/abs/2404.12554

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