Distributed Prescribed-Time Formation Control of Heterogeneous T–S Fuzzy Multiagent Systems: A Hierarchical Design Approach

In this article, the time-varying formation control problem for heterogeneous Takagi–Sugeno (T–S) fuzzy multiagent systems (MASs) is investigated from the perspective of settling time. A leader–follower distributed hierarchical control structure, including communication layer and controller layer, is established. In the communication layer, a distributed prescribed-time observer is constructed to estimate the leader's state and an adaptive law is designed to eliminate the leader's unknown input. In the controller layer, to track the estimate state and achieve time-varying formation control in prescribed time, a new time-varying steady-state zero-error formation manifold with steady-state input is first constructed, then a state feedback prescribed-time fuzzy controller is designed to take the follower's state toward the manifold and reduce the tracking error simultaneously. Furthermore, for the situation where the follower's state is unavailable, an output feedback controller is proposed via the Lyapunov approach and output regulation theory. Sufficient conditions are derived to guarantee that the time-varying formation control of heterogeneous T–S fuzzy MASs can be achieved in prescribed time. Finally, simulation results illustrate the effectiveness of the proposed distributed controllers.