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.

The paper focuses on the problem of formal synthesis of controllers for control-affine nonlinear systems against complex properties. Our goal is to design a closed-form control policy that guarantees the satisfaction of complex properties that are expressed using ( ω)-regular languages and equivalently recognized by Non-deterministic Büchi Automata (NBA). We propose leveraging a funnel-based control approach to provide a closed-form solution to the problem. Our approach decomposes the specification represented by NBA into a sequence of reachability problems which we solve using a funnel-based control approach. Controllers associated with each reachability problem are then combined to design a hybrid control policy enforcing the desired ( ω)-regular property. We demonstrate the effectiveness of the proposed results on room temperature control and mobile robot motion control case studies.