Decentralised adaptive control of a class of hidden leader-follower non-linearly parameterised coupled MASs

In this study, decentralised adaptive control is investigated for a class of discrete-time non-linear hidden leader-follower multi-agent systems (MASs). Different from the conventional leader-follower MAS, among all the agents, there exists a hidden leader that knows the desired reference trajectory, while the follower agents know neither the desired reference signal nor which is a leader agent. Each agent is affected from the history information of its own neighbours. The dynamics of each agent is described by the non-linear discrete-time auto-regressive model with unknown parameters. In order to deal with the uncertainties and non-linearity, a projection algorithm is applied to estimate the unknown parameters. Based on the certainty equivalence principle in adaptive control theory, the control for the hidden leader agent is designed by the desired reference signal, and the local control for each follower agent is designed using neighbourhood history information. Under the decentralised adaptive control, rigorous mathematical proofs are provided to show that the hidden leader agent tracks the desired reference signal, all the follower agents follow the hidden leader agent, and the closed-loop system eventually achieves strong synchronisation in the presence of strong couplings. In the end, the simulation results show the validity of this scheme.