Practical Scalable Synchronization in Leader-Follower Networks of Nonlinear Heterogeneous Agents Using High-Gain Observers

We consider the synchronization problem in the leader-follower framework with a single leader in the network. For a leader-follower network, the smallest eigenvalue of the grounded Laplacian matrix decreases toward zero with an increase in the network size for undirected graphs when the nodes in the graph have bounded neighborhood (fixed number of neighbors) and bounded edge weights. This affects the controller gain of standard nonlinear control approaches used for achieving synchronization as the controller gain is inversely proportional to the smallest eigenvalue of the grounded Laplacian matrix. As a result, it becomes difficult to realize the controllers in practice due to the significant high gain. In this article, we propose a scalable distributed algorithm for the synchronization of second-order nonlinear heterogeneous multiagent systems. First, we assume that the relative state derivates are available for feedback, and we show that the synchronization error can be made arbitrarily small by tuning a particular controller parameter. It is shown that the control signal is bounded uniformly with respect to this controller parameter, and the system performance does not degrade with an increase in network size. Next, we realize the controller using a reduced-order high-gain observer, and we show that the synchronization error can be made arbitrarily small by tuning a controller and observer parameter, respectively. We show that the control signal is bounded uniformly with respect to these parameters. Finally, we demonstrate the efficacy of the proposed controller with two examples: 1) a network of oscillators on the IEEE 300-bus system and 2) a platoon of vehicles.