PDE-based deployment with communicating leaders for a large-scale multi-agent system

We study the deployment of a first-order multi-agent system (MAS) onto a curve in $\mathbb{R}^{n}$. The MAS has a chain topology and two types of agents: leaders and followers. The leaders know their positions relative to the target curve. Neighboring leaders can communicate with one another. Each follower is aware of the intended and existing differences between its state and the states of its two nearest neighbors. To solve the formation control problem, we derive a semi-linear parabolic PDE describing the system when the number of agents is sufficiently large. We derive the stability condition in terms of linear matrix inequalities (LMIs). Using numerical simulations, we demonstrate that increased connectivity between the leaders improves the deployment speed of the MAS.

I. Introduction

Due to its capacity for resolving intricate computational challenges, distributed artificial intelligence (DAI) has remained a prominent topic of interest for researchers globally. DAI can be broadly divided into three classifications based on the methodology employed for task completion. These categories are Multi-Agent Systems (MAS), parallel AI, and Distributed Problem Solving (DPS). Considerable research effort has been dedicated to the control of MAS, which is the principal subject of this paper, owing to its practical usefulness in diverse fields, such as irrigation, the oil industry, UAVs, smart grids, security, satellites, and many more [1].