Decentralized adaptive control of a class of discrete-time nonlinear hidden-leader follower multi-agent systems

In this paper, decentralized adaptive control is investigated for a class of discrete-time nonlinear hidden leader-follower multi-agent systems. Different from the conventional leader-follower multi-agent system, 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 who is a leader. The dynamics of each agent is described by the nonlinear discrete-time auto-regressive model with unknown parameters, and each agent is intrinsically nonlinearly coupled with its neighbors through history information. In order to deal with the uncertainties and nonlinearity, a projection algorithm is applied to identify parameters. Based on the certainty equivalence principle in adaptive control theory, the control law for the hidden leader agent is designed to track the desired reference signal, and the local control law for each follower agent is designed using neighborhood history information. Under the decentralized adaptive control, the hidden leader agent is shown to track the desired reference signal successfully, all the follower agents follow the hidden leader agent, and the closed-loop system eventually achieves strong synchronization under uncertain strong couplings. In the end, the simulation results show the validity of the proposed scheme of decentralized adaptive control.