Time-varying output formation control for linear multi-agent systems with switching topologies

Time-varying output formation control problems for linear multi-agent systems with switching topologies are studied, where two types of switching topologies are considered: (1) the topology is undirected and jointly connected, and 2) each topology is directed and has a spanning tree. An output formation protocol under switching topologies is constructed using the outputs of neighboring agents via dynamic output feedback. Two algorithms are proposed to design the dynamic protocols under both jointly connected topologies and switching directed topologies. Time-varying output formation feasibility conditions are given to describe the compatible relationship among the desired time-varying output formation, the dynamics of each agent, and the switching topologies. The stability of the closed-loop multi-agent systems under the proposed two algorithms is investigated based on the common Lyapunov functional theory and the piecewise Lyapunov functional theory, respectively. In the case where the topologies are jointly connected, time-varying output formation can be achieved for multi-agent systems using the designed protocol if the given time-varying output formation satisfies the feasible constraint. For the case where the switching topologies are directed and have a spanning tree, the time-varying output formation can be realized if the output formation feasibility constraint is satisfied and the dwell time is larger than a positive threshold. Moreover, approaches to determine the output formation references are provided to describe the macroscopic movement of the time-varying output formation. Finally, numerical simulation results are presented to demonstrate the effectiveness of the theoretical results. Copyright (c) 2016 John Wiley & Sons, Ltd.