Time-varying output formation tracking of heterogeneous linear multi-agent systems with multiple leaders and switching topologies

Abstract This paper studies the time-varying output formation tracking problems for heterogeneous linear multi-agent systems with multiple leaders in the presence of switching directed topologies, where the agents can have different system dynamics and state dimensions. The outputs of followers are required to accomplish a given time-varying formation configuration and track the convex combination of leaders’ outputs simultaneously. Firstly, using the neighboring relative information, a distributed observer is constructed for each follower to estimate the convex combination of multiple leaders’ states under the influences of switching directed topologies. The convergence of the observer is proved based on the piecewise Lyapunov theory and the threshold for the average dwell time of the switching topologies is derived. Then, an output formation tracking protocol based on the distributed observer and an algorithm to determine the control parameters of the protocol are presented. Considering the features of heterogeneous dynamics, the time-varying formation tracking feasible constraints are provided, and a compensation input is applied to expand the feasible formation set. Sufficient conditions for the heterogeneous multi-agent systems with multiple leaders and switching directed topologies to achieve the desired time-varying output formation tracking under the designed protocol are proposed. Finally, simulation examples are given to validate the theoretical results.