# Privacy-Preserving Average-Tracking Control for Multi-Agent Systems with Constant Reference Signals

## TL;DR

This paper introduces a new algorithm for multi-agent systems to track an average while preserving privacy, even with constant reference signals.

## Contribution

A novel privacy-preserving integral-type algorithm is proposed with delay-dependent convergence conditions for average-tracking.

## Key findings

- A privacy-preserving algorithm ensures asymptotic average-tracking convergence with constant reference signals.
- The algorithm is extended to handle mismatched reference signals with a new sufficient condition for convergence.
- Numerical simulations confirm the effectiveness of the proposed algorithms.

## Abstract

This paper addresses the average-tracking control problem for multi-agent systems subject to constant reference signals. By introducing auxiliary signals generated from the states and delayed states of agents, a novel privacy-preserving integral-type average-tracking algorithm is proposed. Leveraging the frequency-domain analysis approach, delay-dependent sufficient and necessary conditions for ensuring asymptotic average-tracking convergence are derived. Furthermore, the proposed algorithm is extended to tackle the average-tracking control problem with mismatched reference signals, and a corresponding delay-dependent sufficient condition is established to guarantee privacy-preserving average-tracking convergence. Numerical simulations are conducted to verify the effectiveness of the developed algorithms.