  Developing stable controllers for large-scale networked dynamical systems is
crucial but has long been challenging due to two key obstacles: certifiability
and scalability. In this paper, we present a general framework to solve these
challenges using compositional neural certificates based on ISS (Input-to-State
Stability) Lyapunov functions. Specifically, we treat a large networked
dynamical system as an interconnection of smaller subsystems and develop
methods that can find each subsystem a decentralized controller and an ISS
Lyapunov function; the latter can be collectively composed to prove the global
stability of the system. To ensure the scalability of our approach, we develop
generalizable and robust ISS Lyapunov functions where a single function can be
used across different subsystems and the certificates we produced for small
systems can be generalized to be used on large systems with similar structures.
We encode both ISS Lyapunov functions and controllers as neural networks and
propose a novel training methodology to handle the logic in ISS Lyapunov
conditions that encodes the interconnection with neighboring subsystems. We
demonstrate our approach in systems including Platoon, Drone formation control,
and Power systems. Experimental results show that our framework can reduce the
tracking error up to 75% compared with RL algorithms when applied to
large-scale networked systems.
