Consensus control of higher‐order Lipschitz non‐linear multi‐agent systems based on backstepping method

Abstract

The consensus problem of higher-order Lipschitz non-linear multi-agent systems is studied. For the leaderless case, by using the backstepping method, a distributed recursive linear control scheme is proposed. In the recursive control design, based on feedback domination method, the Lipschitz conditions of the unknown non-linearities are organically used in the virtual controller design. The proposed recursive controllers guarantee that the leaderless multi-agent systems reach global consensus asymptotically. For the leader-follower case, first, baseline distributed recursive controllers are designed via backstepping method and feedback domination technique. Then with the baseline recursive controllers, a kind of linear sliding-mode surface and the corresponding sliding-mode controllers are proposed for the consensus tracking error system. Under the proposed sliding-mode controllers, the leader-follower multi-agent systems reach global consensus asymptotically. Besides, simulations verify the validity of the proposed distributed control algorithms for both cases.