Fixed-time bipartite flocking of perturbed networked UAV systems: A distributed optimization approach

Abstract

Flocking, inspired by the collective dynamics observed in biological swarms, exemplifies the emergence of self-organization and swarm intelligence through local agent interactions. Motivated by these principles, this paper investigates the fixed-time bipartite flocking control problem for networked unmanned aerial vehicle (UAV) systems under external disturbances from the perspective of distributed optimization. The proposed solution addresses key concerns in multi-agent coordination, including the emergence rate of flocking behavior, robustness against uncertainties, and performance optimization. A hierarchical distributed optimal control framework is developed, consisting of a distributed optimization layer and a trajectory tracking layer. Theoretically, the proposed control scheme ensures (i) convergence to the global optimum of the distributed optimization problem within a fixed time, and (ii) fixed-time emergence of bipartite flocking behavior characterized by subgroup cohesion and velocity alignment. The stability of the closed-loop system is rigorously established via a Lyapunov-based analysis method, which also guarantees robustness against dynamic disturbances. In addition, explicit upper bounds on the settling time for both layers are derived, allowing the trade-off between convergence speed and control effort to be tuned through parameter selection. Finally, numerical simulations together with real-world experiments are presented to validate the effectiveness and practical feasibility of the proposed fixed-time bipartite flocking control scheme.