We provide a systematic investigation of using physics-informed neural networks to compute
Lyapunov functions. We encode Lyapunov conditions as a partial differential equation (PDE) …

Transient stability control of power systems is based on actions that are taken automatically
following a disturbance to ensure that the system remains in synchronism. Examples of such …

Motivated by stability analysis of large scale power systems, we describe how the Lasserre
(moment-sums of squares, SOS) hierarchy can be used to generate outer approximations of …

This article derives distributed conditions that guarantee the system-wide stability for power
systems with nonlinear and heterogeneous bus dynamics interconnected via power …

While there has been increasing interest in using neural networks to compute Lyapunov
functions, verifying that these functions satisfy the Lyapunov conditions and certifying …

This thesis deals with approximating sets using Lasserre's moment-SOS hierarchy. The
motivation is the increasing need for efficient methods to approximate sets of secure …

We propose the application of occupation measure theory to the classical problem of
transient stability analysis for power systems. This enables the computation of certified inner …

Operating modern power grids with stability guarantees is markedly important. Typical
methods for analyzing and certifying power grid stability are largely centralized relying on …

Lyapunov functions provide a tool to analyze the stability of nonlinear systems without
extensively solving the dynamics. Recent advances in sum-of-squares methods have …

This article presents a novel numerically tractable technique for synthesizing Lyapunov
functions for equilibria of nonlinear vector fields. In broad strokes, corresponding to an …