Learning Stable and Passive Neural Differential Equations
This addresses stability issues in neural differential equations for applications like control systems, though it appears incremental as it builds on existing PLNet and Hamiltonian dynamics frameworks.
The paper tackles the problem of ensuring stability in neural differential equations by introducing a novel class that is intrinsically Lyapunov stable, exponentially stable, or passive, using a Polyak Lojasiewicz network as a Lyapunov function and parameterizing the vector field as descent directions, with effectiveness demonstrated on a damped double pendulum system.
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.