Distributed formation tracking for high-order multi-agent systems with a leader of unknown input and switching topologies via edge-based adaptive protocol

This paper studies the distributed time-varying formation tracking problems for high-order multi-agent systems with a leader of unknown input and switching topologies. The followers can realize the given formation configuration and track the trajectory of the leader at the same time. By assigning the adaptive gains and the sliding mode terms to each edge of the graph, a novel edge-based adaptive formation tracking protocol is presented to compensate for the leader's unknown input. The proposed approach is fully distributed with no need for the global information of the topology and the upper bound of the leader's input. Based on the common Lyapunov theory, it is proved that the expected formation tracking can be realized by high-order multi-agent systems with arbitrary switching graphs. A simulation example is given to verify the effectiveness of the theoretical results.