Appointed-time consensus: Accurate and practical designs

This paper investigates the appointed-time consensus problem under directed and periodical switching topologies. Here, the appointed finite time means that the consensus arriving time can be off-line pre-assigned according to task requirements without conservative estimation and is independent of the initial conditions of agents' states. From a motion-planning perspective, a novel distributed appointed-time algorithm is developed for a multi-agent system with double-integrator dynamics. Under the assumption that the union of the directed periodical switching topologies contains a directed spanning tree, the proposed distributed algorithms can guarantee the multi-agent system to achieve consensus at an appointed time. Furthermore, the robustness and the practicability of the proposed algorithms are extended. It is the first time here to solve the finite- and appointed-time consensus problem for double-integrator systems under directed switching topologies.