Further Results on Finite-Time Distributed Control of Multiagent Systems With Time Transformation

In previous work, a (smooth) finite-time distributed control algorithm with time transformation was introduced for first-order multiagent systems, which guarantees convergence of the single state of agents to a time-varying leader at a-priori given, user-defined time T from any arbitrary initial conditions with bounded local control signals. In this paper, we present an extension of this previous work to second-order multiagent systems. Specifically, utilizing a user-defined finite-time interval of interest t ∈ [0, T), we time transform this class of multiagent systems subject to the considered (smooth) distributed control algorithm to an infinite-time interval s ∈ [0, ∞) with s being the stretched time. Based on a property of this time transformation, this results in finite-time convergence as the regular time t approaches to T from any arbitrary initial conditions with bounded local control and internal signals. Finally, two numerical examples illustrate the efficacy of the proposed algorithm.