Abstract: Flying Ad-Hoc Network(FANET) which is a field of wireless Ad-Hoc network formed by small unmanned aerial vehicles(UAVs),is critical in achieving UAV swarm system.Beacon mechanism in FANET plays the fundamental role in performing consensus behavior of UAV swarm.However,the wireless link failures of practical FANET will introduce beacon loss which will affect the convergence rate or convergence time,which describe how fast all UAV states reach the common value.To achieve optimal consensus behavior,it is important to know how beacon mechanism affects the consensus behavior.To solve above-mentioned problem,this paper has investigated the analytical relation between the convergence rate/time of consensus behavior and the beacon loss probability.In the analytical work,information flow topology at each period is modeled by random directed graph,and one indicator matrix weighted is designed to model the Laplacian matrix of the graph.Based on the knowledge of matrix theory and spectrum radius of a matrix,the analytical work in this paper firstly gives an analytical expression of expected consensus va-lue of the consensus process.Utilizing the expected consensus value,a novel quantification of convergence rate based on the expected final consensus value is provided.Different from existing analytical work,the convergence rate is quantified based on the expected consensus value,rather than to the average value of all states at each period.Finally,utilizing the knowledge of matrix theory and spectrum radius of a matrix,the proposed analytical work analyzes the relation between the convergence rate/time and the beacon loss probability.Simulation results show that,the proposed analytical model can accurately capture the convergence rate along with time in practical FANETs.Moreover,the proposed model can accurately capture the effect of average link failure probability on each link,initial state distribution and the number of UAVs on the convergence time.Moreover,compared with exis-ting analytical model,the proposed analytical model can capture the convergence performance in practical FANET more precisely.

Key words: Consensus control algorithm, Convergence rate, Convergence time, Flying Ad-Hoc Network, Random directed graph