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.