Group consensus for discrete-time multi-agent systems based on iterative learning control

In this paper, the problem of perfect group consensus tracking is discussed for first-order discrete-time multi-agent systems with linear and nonlinear dynamic under directed communication topology. First of all, for first-order discrete-time linear and nonlinear multi-agent systems with two subgroups, distributed control protocols are constructed using iterative learning control method, based on matrix theory and compression mapping principle, sufficient conditions are derived to achieve perfect group consensus tracking under the proposed control protocol. The novel initial state learning laws are proposed, which can make each follower agent with arbitrary initial state and track the corresponding leader as iteration number approaches infinity. Secondly, we extend the corresponding results to the case of multiple subgroups. Then the formation control with multiple subgroups is also considered. Finally, three numerical examples are given to demonstrate the validity of the results.