Optimal interconnection design for leader-follower coordination with noise

In this study, we address a leader-follower coordination problem with noise in a multi-agent system. In order to minimise the mean-square deviation of the individual state of followers from the state of the leader, we develop a strategy to select a subset of followers to connect with the leader. We adopt the method of convex optimisation to solve both constant edge weight and different edge weight case. Furthermore, we propose optimised algorithms to find the fastest convergence speed. We also study optimisation problems for leader-follower system with a dynamic leader, and also provide a sufficient condition for the convergence of the expected value of the total mean-square deviation. Examples and applications of the developed methodology are also discussed.