Global Optimal Consensus for UAV Swarms With Time-Varying Objective Functions and Bounded Input Constraints

This paper investigates a distributed time-varying optimization problem concerning UAV swarm systems with bounded inputs. The objective is to achieve state consensus and minimize the sum of local time-varying objective functions in a distributed manner, while considering the constraints on inputs. To address this problem, we propose a distributed optimization protocol utilizing the projection operator and prediction-correction method. This protocol enables the UAVs to track the time-varying optimal solution with an asymptotically diminishing error. It is shown that the proposed protocol achieves approximate global optimal consensus for UAVs with different connected communication topologies, including undirected, directed detail-balanced, and switching topologies. Consequently, the UAV swarm, equipped with the proposed protocol, can establish a predetermined formation and effectively track moving targets. To validate the theoretical findings, we present three applications: a scalar example, a cooperative hunting task, and swarm tracking behavior.