Finite-time distributed control with time transformation

In this article, we propose distributed control algorithms for first- and second-order multiagent systems for addressing finite-time control problem with a priori given, user-defined finite-time convergence guarantees. The proposed control frameworks are predicated on a recently developed time transformation approach. Specifically, our contribution is twofold: First, a generalized time transformation function is proposed that converts the user-defined finite-time interval to a stretched infinite-time interval, where one can design a distributed control algorithm on this stretched interval and then transform it back to the original finite-time interval for achieving a given multiagent system objective. Second, for a specific time transformation function, we analytically establish the robustness properties of the resulting finite-time distributed control algorithms against vanishing and nonvanishing system uncertainties. By contrast to existing finite-time approaches, it is shown that the proposed algorithms can preserve a priori given, user-defined finite-time convergence regardless of the initial conditions of the multiagent system, the graph topology, and without requiring a knowledge of the upper bounds of the considered class of system uncertainties. Illustrative numerical examples are included to further demonstrate the efficacy of the presented results.