Multi-agent Consensus Tracking with Initial State Error by Iterative Learning Control

This work addresses a leader-follower tracking problem by an iterative learning control approach. In the multi-agent setup, a dynamic leader is connected to a few of followers, and the communication among agents is described by a directed graph. In contrast to many existing literature in which the perfect initial condition is imposed, we assume that the initial state is reset to a fixed position that is not equal to the desired state. First, the performance of D-type learning rule is analyzed, and it is shown that the follower's output trajectory converges to a unique trajectory. In particular, when the learning gain is full column rank the trajectory of each agent converges to the leader's trajectory with a constant shift. Next, to improve the control performance, PD-type learning rule is proposed for the tracking problem. It is proven that the output trajectory converges exponentially to the leader's trajectory for each agent provided that the learning gains are appropriately chosen. Finally, numerical examples are presented to demonstrate the theoretical results.