Learning Stable and Passive Neural Differential Equations

arXiv:2404.12554v1 Announce Type: cross
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 …

abstract arxiv class cs.lg cs.sy differential differential equation eess.sy equation function network novel paper type vector