Consensus Control via Iterative Learning for Singular Multi-Agent Systems With Switching Topologies

For the state consensus tracking of the singular multi-agent system, under the condition of the communication topology randomly switching only along time axis but unchanging along iteration axis, a distributed iterative learning control protocol is proposed. By singular value decomposition method, the singular multi-agent system is transformed into differential algebra system, and thus the state of the system is accordingly divided into two parts. Then applying the derivative of the tracking error for the first part of the state and the tracking error of the second part of the state and combining the switching topology graph, the distributed iterative learning control protocol is constructed. Furthermore, the convergence of the proposed algorithm is proved by the compression mapping method, and the convergence conditions of the algorithm are obtained. The proposed algorithm can make the state gradually approach the desired state with the increase of iterations. When the number of iterations is sufficient large, the state of each agent can completely track the desired state over a finite time interval. Finally, the simulation examples are given to further validate the effectiveness of the proposed algorithm.