Consensus Tracking via Iterative Learning for Multi-Agent Systems With Random Initial States

In this paper, a distributed consensus iterative learning control algorithm is proposed for the finite-time consensus tracking of multi-agent systems with random initial states. The tracking errors from the agent itself and its neighbours are applied to successively rectify the control protocol when only some agents can obtain the desired trajectory information. Additionally, a time interval is designed in the control protocol, and the random initial state errors are rectified, one-by-one, in the time interval. The interval can gradually shorten as the number of iterations increases. Furthermore, the convergence of the algorithm is theoretically proven by the contraction mapping method, and the convergence condition is derived. The proposed algorithm can cause the time interval to gradually shorten with the iterations increase, during the time, the desired trajectory cannot be consistently tracked due to the random initial state errors. As a consequence, the algorithm gradually widens the time interval for full consensus tracking of the multi agents. Finally, the simulation examples are provided to verify the effectiveness of the algorithm.