Fully Distributed Finite-Time Formation Tracking of Heterogeneous Multi-Agent Systems Under Directed Networks

This paper considers the finite-time formation tracking of high-order heterogeneous multi-agent systems (HMASs), where the communication network among agents is directed and the leader’s input is unknown to all followers. An innovative fully distributed finite-time control strategy, independent of global topological information, is proposed. First, a fully distributed observer is constructed to estimate leader’s state in finite time, despite leader’s unknown input. It is noted that an adaptive gain is wisely designed for the observer such that global topological information is no longer necessary. However, due to the asymmetry of the Laplacian matrix and the fact that the adaptive gain may not converge to its ideal value, the commonly used finite-time convergence criteria are not applicable to our case, and achieving the finite-time convergence of the observer becomes rather challenging. To overcome technical obstacles, a suitable Lyapunov function is specifically constructed, and then the desired finite-time convergence is established with the aid of a contradiction argument. Further, a disturbance observer is designed by utilizing the state transformation, which is able to estimate the composite disturbances consisting of both external disturbances and the leader’s unknown input. Finally, an observer-based formation controller is proposed to achieve the desired configuration. It is guaranteed that zero formation error, rather than just a neighbor of zero, can be realized in finite time through chattering-free control signals. Simulations are performed to verify the effectiveness of the proposed algorithm.