A Distributed Optimization Algorithm for Fixed-Time Flocking of Second-Order Multiagent Systems

In this article, a distributed optimization algorithm with fixed-time flocking is proposed for continuous-time multi-agent system with double-integrator dynamics. This algorithm has the ability to jointly drive the agents toward a common velocity while optimizing the global objective function. Moreover, based only on local information and communication, the fixed-time flocking and convergence are reported, and the upper bounds of the settling time are given, respectively. This significantly improves the consensus and convergence speed of the algorithm, which only needs the adjustment of parameters. In addition, the event-triggered mechanism is introduced to reduce the energy required for agent communication. It is verified that, under certain conditions, such an event-triggered algorithm can still ensure fixed-time flocking and convergence, and Zeno behavior is strictly prohibited. Besides, the fixed-time distributed algorithm is further adapted to accommodate time-varying communication conditions, where the communication topologies are switching within a series of undirected and connected graphs. Finally, two numerical examples are given to demonstrate the effectiveness of the theoretical analysis.