Distributed PID Control for Consensus of Homogeneous and Heterogeneous Networks

TL;DR

This paper proposes a distributed PID control strategy to achieve consensus in both homogeneous and heterogeneous linear networks, with proven convergence and demonstrated effectiveness on a power grid model.

Contribution

It introduces a novel distributed PID approach for consensus in diverse linear networks, with rigorous convergence proofs and practical validation.

Findings

Proven convergence of the distributed PID control in both network types.

Successful application to a power grid model demonstrating practical effectiveness.

Theoretical results supported by Lyapunov-based analysis.

Abstract

We investigate the use of distributed PID actions to achieve consensus in networks of homogeneous and heterogeneous linear systems. Convergence of the strategy is proved for both cases using appropriate state transformations and Lyapunov functions. The effectiveness of the theoretical results is illustrated via its application to a representative power grid model recently presented in the literature.