Switching topology-based nonlinear uncertain multiagent systems with unstable leader under model reference adaptive hierarchical control

This paper addresses the leader–follower consensus problem for high-order heterogeneous nonlinear uncertain multiagent systems under a switching topology and unknown external disturbances. A novel model reference adaptive hierarchical control is proposed, whose controller only requires knowledge of the followers' states. Conventional model reference adaptive control selects reference models for all followers under a fixed topology and relies on global topology information. In contrast, to the best of the authors' knowledge, switching topology-based virtual reference models have not been developed for non-leader-fixed followers; this paper proposes such a model for followers that cannot directly retrieve leader information. This design also resolves the challenge that the virtual reference models switch according to local topology information. Moreover, a lower bound on the minimum number of leader-fixed followers is established, its quantitative relationship with the switching topology is characterised, and a sufficient condition for attaining this lower bound is provided. Based on the proposed model reference adaptive hierarchical control, a leader with unstable dynamics is considered for nonlinear uncertain multiagent systems, and sufficient conditions for achieving consensus are introduced. Finally, a numerical simulation illustrates the effectiveness of the theoretical results.