Distributed Time-Varying Output Formation Tracking for Heterogeneous Linear Multiagent Systems With a Nonautonomous Leader of Unknown Input

This paper studies the time-varying output formation (TVOF) tracking problems for heterogeneous linear multiagent systems with a nonautonomous leader on directed topologies, where the dynamics of the agents can be different in the aspects of both parameters and dimensions, and the leader can have unknown control input. A TVOF tracking protocol and a design algorithm are presented using the neighboring interaction. In the proposed protocol, a distributed observer with adaptive updating mechanism is constructed for each follower to asymptotically estimate the state of the leader under the influences of the leader's unknown input first. Then, a local formation controller is presented by utilizing the distributed observer, the local state observer, and the desired formation vector. Based on the Lyapunov stability theory, it is proved that the expected TVOF tracking can be accomplished by the heterogeneous multiagent systems in the presence of the leader's unknown input. Furthermore, a continuous TVOF tracking protocol with sigma-modification adaptive law is proposed to avoid the large chattering phenomenon.