An LQG motivated leader-follower consensus with uncertainty

This paper addresses the leader-follower consensus problem in discrete time under fixed and time-invariant communication topology. Each agent follows a general linear dynamic and is equipped with a local Kalman estimator. While many literature illustrated a lower bound for convergence in continuous time, with similar form of feedback controller, we show that there exist an upper bound in coupling gain for the fixed gain controller. A novel distributed adaptive controller is also introduced, which only depends on local estimation of eigenvalue and neighbors' information. The performance and convergence speed of the proposed protocol are analyzed, and is demonstrated with numerical simulations.