Finite-time Consensus for Second-order Multi-agent Systems Based on Embedded Control

This paper studies the finite-time consensus problem for both leader-follower and leaderless second-order multi-agent systems. To solve the problem, a nonsmooth embedded control scheme is used, which is made up of two parts. In part one, for each case, based on nonsmooth control theory, a distributed virtual signal generator is designed. For the leaderless case, the outputs of the designed generator reach finite-time consensus and for the leader-follower case, virtual position and velocity signals of the designed generator track the leader's position and velocity in finite time. In part two, for each case, through embedding the generator into the feedback loop and taking its outputs (i.e., outputs for the leaderless case and virtual position and velocity signals for the leader-follower case) as the reference outputs for the agents (i.e., all the agents for the leaderless case and the followers for the leader-follower case), some tracking controllers are designed for the agents to track their reference outputs in finite time. Based on this scheme, some consensus algorithms are proposed. Under the proposed consensus algorithms, leaderless and leader-follower multi-agent systems achieve finite-time consensus. Numerical simulations verify the validity of the proposed consensus algorithms.