Exponential Consensus through Z-Control in High-Order Multi-Agent Systems

TL;DR

This paper presents a Z-control method for high-order multi-agent systems that guarantees exponential consensus convergence while maintaining average dynamics, applicable to various models like opinion and flocking systems.

Contribution

It introduces a novel Z-control framework for arbitrary order multi-agent systems, supporting both direct and indirect control schemes with proven exponential convergence.

Findings

Demonstrates robustness of Z-control in opinion dynamics.

Shows effectiveness in Cucker-Smale flocking models.

Validates theoretical results through numerical experiments.

Abstract

In this work, we introduce a Z-control strategy for multi-agent systems of arbitrary order, aimed at driving the agents toward consensus in the highest-order observable state. The proposed framework supports both direct and indirect control schemes, making it applicable in scenarios where high-order derivatives such as acceleration cannot be directly manipulated. Theoretical analysis ensures exponential convergence while preserving the average dynamics, and a hierarchy of control laws is derived accordingly. Numerical experiments up to third-order models, including opinion dynamics and Cucker-Smale flocking systems, demonstrate the robustness and flexibility of Z-control under varying interaction regimes and control intensities.