Cooperative tracking and estimation of linear multi-agent systems with a dynamic leader via iterative learning

This paper presents a new iterative learning design approach for cooperative tracking and estimation of linear multi-agent systems with a dynamic leader. The input of the dynamic leader is unavailable to all follower agents. Distributed iterative learning controllers, based on the relative state information of neighbouring agents, are proposed for tracking the dynamic leader, and meanwhile identifying the unknown input of the leader. Stability and convergence of the proposed controller are established using Lyapunov-Krasovskii theory. Further, this result is extended to the output feedback case where only partial states can be measured. A local observer is constructed to recover the unmeasurable states. Then, distributed iterative learning tracking controllers, based on the relative observed states of neighbouring agents, are devised. For both cases, the main advantage of the proposed controllers allows for tracking the dynamic leader for undirected graphs without knowing the input of the leader, and meanwhile identifying the unknown input of the leader using distributed iterative learning laws. An example is given to show the efficacy and utility of the theoretical results.