Leader-Follower Flocking for Discrete-Time Cucker-Smale Models with Lossy Links and General Weight Functions

In this article, we investigate leader-follower flocking for the Cucker-Smale model with lossy links and general weight functions. Here, the loss phenomenon of the control packages from the controller to the actuator is characterized by a Bernoulli stochastic variable and the edge weights of the interaction network are determined by a general update rule based on the distance between agents. A method based on the products of substochastic matrices is developed to analyze the flocking behavior with lossy links. By means of this method, a sufficient condition which depends on the agents' initial states, the topology structure, the successful information transmission rate and the weight function is established. Compared with the previous Cucker-Smale flocking results, which are only applicable to positive and decreasing weight functions with specific forms, our result is more general and can be applied to arbitrary positive and decreasing weight functions with nonzero lower bounds. Finally, our result is illustrated through a simulation example.