Modification and comparative analysis of smooth control laws for a group of agents

We consider the control problem for a group containing a given number of uninformed agents; this is a consensus problem. An agent's model is defined by a two-dimensional integrator. The purpose of this work is to synthesize a decentralized smooth law of the agents' motion in a multiagent system that would let us construct and support a prescribed configuration of the group of agents. The considered group should follow the leader, either real or virtual. Informational links between agents are given by a communications digraph. The work shows numerical results for various initial conditions and various desired trajectories.