Encirclement Control for PDE-Based Leader-Follower Multi-Agent Systems with Targets in a Sphere: Part 2 – Rotation Encirclement

This paper introduces an innovative rotating encirclement control designed for parabolic Partial Differential Equation (PDE)-based multi-agent systems. The derivation of the PDE-based continuum multi-agent system model stems from techniques in flow system theory. The control strategy involves multi-step control within the domain and boundaries consisting of 2 parts. Initially in part 1, a successful target-enclosing control was applied to the system. After successfully achieving enclosing, here in part 2 of the paper, the agents face further challenges, including rotating around targets and adjusting their formation to maintain the encirclement. To address these challenges, in-domain control is applied to the agents, ensuring compliance with all requirements. Employing successive multi-step controls in a distributed manner is crucial for improving tracking and coordination among the agents, thus enhancing the effectiveness of the encirclement control. Stability analysis of the closed-loop system is conducted using the Lyapunov technique. Finally, simulations are conducted to evaluate the effectiveness of our proposed methodology. It is worth mentioning that part 2 stands as an independent outcome, tackling the challenge of rotating encirclement by leveraging a target-enclosing formation.