Decentralized adaptive synchronization of a class of discrete-Time nonlinear multi-Agent systems with unknown parameters and high-frequency gains

This paper addresses the challenging problem of decentralized adaptive control for a class of coupled hidden leader-follower multi-Agent systems, in which each agent is described by a nonlinearly parameterized uncertain model in discrete time and can interact with its neighbors via its available information on its neighbors. One of the agents is a leader, who knows the desired reference trajectory, while other agents have no access to the desired reference signal or are unaware of existence of the leader. In order to tackle unknown internal parameters and unknown high-frequency gains, a projection-Type parameter estimation algorithm is proposed. Based on the certainty equivalence principle and neighborhood history information, the decentralized adaptive control is designed, under which, the boundedness of identification error is guaranteed with the help of the Lyapunov theory. Under some conditions, the multi-Agent system eventually achieves strong synchronization in the presence of strong couplings. Finally, a simulation example is given to support the results of the proposed scheme.