A travelling wave approach to a multi-agent system with a path-graph topology

TL;DR

This paper introduces a wave-based analysis and control method for multi-agent systems with path-graph topology, enabling stability and performance improvements through feedback controllers that manage wave reflections.

Contribution

It develops a novel wave transfer function approach for analyzing agent interactions and designs controllers to mitigate wave reflections, enhancing system stability.

Findings

Achieves asymptotic stability of the multi-agent system.

Ensures string stability through feedback control.

Effectively compensates for wave reflections and transient effects.

Abstract

The paper presents a novel approach for the analysis and control of a multi-agent system with non-identical agents and a path-graph topology. With the help of irrational wave transfer functions, the approach describes the interaction among the agents from the `local' perspective and identifies travelling waves in the system. It is shown that different dynamics of the agents creates a virtual boundary that causes a partial reflection of the travelling waves. Undesired effects due to the reflection of the waves, such as amplification/attenuation, long transients or string instability, can be compensated by the feedback controllers introduced in this paper. We show that the controllers achieve asymptotic and even string stability of the system.