Distributed neuro‐adaptive control protocols for non‐strict feedback non‐linear MASs with input saturation

This study develops distributed neuro‐adaptive control protocols for synchronisation of leader–follower multi‐agent systems (MASs) with non‐linear dynamics in non‐strict‐feedback form. The communication graph is assumed to be directed, and the agents are considered heterogeneous. The leader's dynamics are also assumed non‐linear, and the state derivative of the leader is unknown to its immediate followers. The well‐known command filtered backstepping approach, presented for single‐agent systems in the literature, is extended to the synchronisation of MASs with non‐strict‐feedback non‐linear dynamics. This obviates the requirement of computing the n th‐order derivatives of the local neighbourhood synchronisation error at the step n of the design. The number of adaptive tuning laws and consequently the complexity of the neuro‐adaptive design is reduced by estimating only a positive scalar related to unknown non‐linear dynamics of each agent. An auxiliary system is then introduced into the control design to compensate for the discrepancy between designed and saturated control signals. The proposed distributed control protocol guarantees that all signals in the closed‐loop system are cooperatively semi‐globally uniformly ultimately bounded, and the consensus error for all agents converge to a small neighbourhood of the origin. Finally, a simulation example demonstrates the effectiveness of the proposed control scheme.