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.