Decentralized adaptive consensus control for discrete-time heterogeneous semiparametric multiagent systems

Different from the consensus control of traditional multiagent systems, this paper studies the decentralized adaptive consensus control for discrete-time heterogeneous hidden leader-following semiparametric multiagent system, in which the dynamic equation of each agent has both parametric uncertainties and nonparametric uncertainties. In the considered system, there is a hidden leader agent who can receive the reference signal, but it can only affect the states of those agents who are in its neighborhood. For other following agents, they do not know the leader's existence or the reference signal, and they can only receive information from their neighbors. Our goal is to design decentralized adaptive controllers to make sure that all agents can track the reference signal, and the closed-loop system achieves consensus in the presence of mutual coupling relations. Due to the existence of both parametric and nonparametric uncertainties in the system, we need to estimate them separately. For the parametric part, we propose a novel dead zone with threshold converging to zero to modify the traditional gradient update law, while for the nonparametric part, we introduce an auxiliary variable including both two uncertainties to facilitate the nonparametric uncertainties compensation. Based on the certainty equivalence principle in adaptive control theory, the decentralized adaptive controller is designed for each agent to make sure that all of them can track the reference signal. Finally, under the proposed control protocol, strict mathematical proofs are given by using Lyapunov theory; then, simulation results are provided to demonstrate the effectiveness of proposed decentralized adaptive controllers.