Leader-follower synchronization and ISS analysis for a network of boundary-controlled wave PDEs

TL;DR

This paper studies a network of wave PDE agents with boundary control, proposing a linear protocol that guarantees exponential synchronization and ISS robustness against disturbances, using Lyapunov analysis.

Contribution

It introduces a novel boundary control protocol for wave PDE networks with leader-follower synchronization and provides ISS analysis for disturbance effects.

Findings

Exponential synchronization is achieved under the proposed protocol.

A simple tuning rule guarantees exponential convergence.

An ISS relation quantifies disturbance effects on tracking accuracy.

Abstract

A network of agents, modeled by a class of wave PDEs, is under investigation. One agent in the network plays the role of a leader, and all the remaining "follower" agents are required to asymptotically track the state of the leader. Only boundary sensing of the agent's state is assumed, and each agent is controlled through the boundary by Neumann-type actuation. A linear interaction protocol is proposed and analyzed by means of a Lyapunov-based approach. A simple set of tuning rules, guaranteeing the exponential achievement of synchronization, is obtained. In addition, an exponential ISS relation, characterizing the effects on the tracking accuracy of boundary and in-domain disturbances, is derived for the closed loop system.