Learning Stable and Passive Neural Differential Equations
<|reference_start|>Learning Stable and Passive Neural Differential Equations: 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.<|reference_end|>
@article{cheng2024learning,
    title={Learning Stable and Passive Neural Differential Equations},
    author={Jing Cheng, Ruigang Wang, Ian R. Manchester},
    journal={arXiv preprint arXiv:2404.12554},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.12554},
    primaryClass={eess.SY cs.LG cs.SY}
}