Distributed Learning-based Stability Assessment for Large Scale Networks of Dissipative Systems

Abstract

We propose a new distributed learning-based framework for stability assessment of a class of networked nonlinear systems, where each subsystem is dissipative. The aim is to learn, in a distributed manner, a Lyapunov function and associated region of attraction for the networked system. We begin by using a neural network function approximation to learn a storage function for each subsystem such that the subsystem satisfies a local dissipativity property. We next use a satisfiability modulo theories (SMT) solver based falsifier that verifies the local dissipativity of each subsystem by determining an absence of counterexamples that violate the local dissipativity property, as established by the neural network approximation. Finally, we verify network-level stability by using an alternating direction method of multipliers (ADMM) approach to update the storage function of each subsystem in a distributed manner until a global stability condition for the network of dissipative subsystems is satisfied. This step also leads to a network-level Lyapunov function that we then use to estimate a region of attraction. We illustrate the proposed algorithm and its advantages on a microgrid interconnection with power electronics interfaces.