Multi‐rate sampled‐data algorithm for leader–follower flocking

Abstract

This work presents a new algorithm for flocking with a virtual leader by introducing a new sampling scenario, so-called multi-rate sampling. In the multi-rate sampling, the period of receiving data from different sources is different, but the updating time for all individuals is the same. Here, the authors assume that the period of receiving data from neighbour agents is T, and that from the virtual leader is an integer multiple of it, that is, mT. An upper bound for period T is attained from the upper bound of the energy function that guarantees the neighbouring network to be connected and collision to be avoided between agents. Also, an upper bound on m, which ensures the velocity of informed and uninformed agents to tend the virtual leader's velocity, is derived. The convergence analysis demonstrates that whatever the acquiring period of the virtual leader's information mT is further, then the convergence rate of the group's velocity to the virtual leader's velocity will be greater. Finally, to show the validity of the results, they present a simulation.