This technical note addresses the distributed consensus protocol design problem for multi-agent systems with general linear dynamics and directed communication graphs. Existing works usually design consensus protocols using the smallest real part of the nonzero eigenvalues of the Laplacian matrix associated with the communication graph, which however is global information. In this technical note, based on only the agent dynamics and the relative states of neighboring agents, a distributed adaptive consensus protocol is designed to achieve leader-follower consensus in the presence of a leader with a zero input for any communication graph containing a directed spanning tree with the leader as the root node. The proposed adaptive protocol is independent of any global information of the communication graph and thereby is fully distributed. Extensions to the case with multiple leaders are further studied.

Distributed consensus tracking is addressed in this paper for multi-agent systems with Lipschitz-type node dynamics. The main contribution of this work is solving the consensus tracking problem without the assumption that the topology among followers is strongly connected and fixed. By using tools from M-matrix theory, a class of consensus tracking protocols based only on the relative states among neighboring agents is designed. By appropriately constructing Lyapunov function, it is proved that consensus tracking in the closed-loop multi-agent systems with a fixed topology having a directed spanning tree can be achieved if the feedback gain matrix and the coupling strength are suitably selected. Furthermore, with the assumption that each possible topology contains a directed spanning tree, it is theoretically shown that consensus tracking under switching directed topologies can be achieved if the control parameters are suitably selected and the dwell time is larger than a positive threshold. The results are then extended to the case where the communication topology contains a directed spanning tree only frequently as the system evolves with time. Finally, some numerical simulations are given to verify the theoretical analysis.

The problem of distributed formation control for multiple quadrotor aircraft in the form of leader-follower structure is considered in this paper. Based on a nonsmooth backstepping design, a novel consensus formation control algorithm is proposed and utilized. First, for the position control subsystem, based on the linear quadratic regulator optimal design method, a formation control law for multiple quadrotor aircraft is designed such that the positions of all the quadrotor aircraft converge to the desired formation pattern. The designed formation control law for position systems will generate the desired attitude for the attitude control systems. Second, for the attitude control subsystem described by unit quaternion, by employing the technique of finite-time control and switch control, a global bounded finite-time attitude tracking controller is designed such that the desired attitude can be tracked by the multiple quadrotor aircraft in finite time. Finally, numerical example is performed to demonstrate that all quadrotor aircraft converge to the desired formation pattern in the 3-D-space.