This study considers the consensus tracking problem of singular multi‐agent systems by using an iterative learning control approach. Here, the communication among the followers is described by a directed graph, and only a portion of the followers can receive the leader's information. For such singular multi‐agent systems, a unified iterative learning algorithm is proposed in both continuous‐time domain and discrete‐time domain. Furthermore, the convergence condition of the algorithm is presented and analysed. In this study, the main contribution is to extend the iterative learning control theory from multi‐agent systems to singular multi‐agent systems. It is shown that the algorithm can guarantee the outputs of the followers converge to the leader's trajectory on a finite time interval along the iteration axis. Finally, the provided examples illustrate the effectiveness of the theoretical results.

Based on Nesterov accelerated gradient method, the problem of iterative learning control for a class of linear discrete-time systems is considered in this paper. Firstly, the iterative learning control problem of linear discrete-time systems is transformed into an iterative least-squares problem. Then, the Nesterov accelerated gradient method is introduced into the iterative learning control framework. Note that the Nesterov accelerated gradient learning algorithm has the capability of fast convergence. It is shown that the algorithm presented in this paper can guarantee the output tracking error converges to zero with rate O(1/k), where k is the iteration counter. Moreover, the monotonic convergence of the Nesterov accelerated gradient learning algorithm is analyzed and discussed. Finally, the effectiveness of the proposed method is verified by two simulation examples.

Based on a specific decomposition of discrete singular systems, in this paper, we study the problem of state tracking control by using PD-type algorithm of iterative learning control. The convergence conditions and theoretical analysis of the PD-type algorithm are presented in detail. An illustrative example supporting the theoretical results and the effectiveness of the PD-type iterative learning control algorithm for discrete singular systems is shown at the end of the paper.