Practical Multi-Cluster Consensus for Euler-Lagrangian Systems with Unknown Parameters using Prescribed Performance Control

The paper addresses the challenge of achieving practical multi-cluster consensus among agents interacting through a matrix-weighted graph. The objective is to coordinate the agents to effectively capture or escort a moving target. Each agent satisfies Euler-Lagrange (EL) dynamics, whose parameters may be unknown, and is subject to external disturbances. We propose a multi-cluster control framework that ensures all agents within a cluster converge to a common trajectory, while individual clusters maintain a specific formation around the moving target. A prescribed performance control scheme is developed to guarantee that relative state trajectories remain within user-defined performance bounds throughout the task. The closed loop system under the proposed control scheme is analytically proven to achieve practical multi-cluster consensus and satisfaction of user-defined performance bounds without requiring knowledge of system parameters. The proposed framework supports various consensus scenarios, including consensus, bipartite consensus, and multi-cluster consensus, offering flexibility in adjusting both the number of clusters and the number of agents in each cluster. We provide numerical simulations to validate the theoretical results.