Robustness of Finite-Time Distributed Control Algorithm with Time Transformation

The focus of this paper is distributed control of multiagent systems in a-priori given, user-defined finite-time interval using a recently developed time transformation approach. In particular, we utilize a time transformation function to convert a user-defined finite-time interval to a stretched infinite-time interval such that a distributed control algorithm can be designed on this stretched interval and then it can be transformed back to the original finite-time interval in order to satisfy a given multiagent system objective. In addition, the robustness of the resulting finite-time distributed control algorithm against vanishing and non-vanishing system uncertainties is also discussed. In contrast to existing finite-time approaches, the presented algorithm can preserve apriori given, user-defined finite-time convergence regardless of the initial conditions of the multiagent system and without the need for a knowledge of the upper bounds of the considered system uncertainty classes.