Practical Prescribed Performance Multi-Cluster Consensus for Euler–Lagrangian Systems With Unknown Parameters

The paper addresses the challenge of achieving practical multi-cluster consensus among agents interacting through a matrix-weighted graph. The objective is to coordinate multiple agents to capture or escort a moving target while forming distinct clusters around it. Each agent is modeled by Euler-Lagrange (EL) dynamics with unknown parameters and is subject to external disturbances. A distributed multi-cluster control framework is proposed in which agents within the same cluster converge to a common trajectory, while different clusters maintain prescribed formations around the target. To ensure reliable performance, a prescribed performance control scheme is incorporated, guaranteeing that relative state trajectories remain within user-defined 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. The effectiveness of the proposed approach is verified through numerical simulations, where twelve agents achieve multiple formations around a target while strictly adhering to user-defined performance functions. Real-time hardware experiments, conducted with a team of five differential-drive robots forming a triangular formation, further validate the proposed control strategy.