Reduced-order observer-based distributed tracking control for high-order multi-agent systems with heterogeneous leader

This paper considers distributed tracking control of leader-follower multi-agent systems with directed communication topologies. The directed communication graph needs to contain a spanning tree. It is supposed that the leader has the different internal dynamic with the followers, and each agent cannot measure the states׳ information of itself and its neighbors directly. Therefore a reduced-order observer is designed for the first time for the multi-agent systems which contains the external disturbance by using an appropriate transformation, and the state information of the agents can be divided into the measurable and unmeasurable parts. Then, distributed observer-based consensus protocols are proposed such that all the outputs of the followers reach a same trajectory with the leader׳s output, based on the relative outputs of neighboring agents. A multi-step algorithm is presented to construct the observer-based protocols. In light of the discrete-time algebraic Riccati equation and internal model principle, output synchronization problem is completed. The result is also extended to the continuous-time multi-agent systems. At last, numerical simulations are provided to verify the effectiveness of the theoretical results.