Neural Distributed Controllers with Port-Hamiltonian Structures

TL;DR

This paper introduces neural distributed controllers based on port-Hamiltonian structures that ensure stability and robustness in large-scale nonlinear systems, enabling effective training without parameter constraints.

Contribution

It leverages port-Hamiltonian structures to design neural controllers with guaranteed stability and finite gain, simplifying training and improving robustness in distributed control.

Findings

Controllers guarantee closed-loop stability and finite $\\mathcal{L}_2$ gain.

Effective training with standard stochastic gradient descent.

Successful numerical demonstration on Kuramoto oscillators.

Abstract

Controlling large-scale cyber-physical systems necessitates optimal distributed policies, relying solely on local real-time data and limited communication with neighboring agents. However, finding optimal controllers remains challenging, even in seemingly simple scenarios. Parameterizing these policies using Neural Networks (NNs) can deliver good performance, but their sensitivity to small input changes can destabilize the closed-loop system. This paper addresses this issue for a network of nonlinear dissipative systems. Specifically, we leverage well-established port-Hamiltonian structures to characterize deep distributed control policies with closed-loop stability guarantees and a finite $\mathcal{L}_2$ gain, regardless of specific NN parameters. This eliminates the need to constrain the parameters during optimization and enables training with standard methods like stochastic gradient descent. A numerical study on the consensus control of Kuramoto oscillators demonstrates the effectiveness of the proposed controllers.