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.

Automated summary

This article proposes distributed control algorithms for multiagent systems using a time transformation approach to convert finite-time intervals to infinite-time intervals, achieving system objectives while maintaining robustness against uncertainties. The algorithms are shown to preserve user-defined finite-time convergence guarantees regardless of initial conditions, graph topology, or knowledge of system uncertainties.