Scalable Input-to-State Stability of Heterogeneous Systems With Applications in Vehicle Platooning

This work studies the scalability of interconnected nonlinear systems composed of possibly heterogeneous subsystems. To this purpose, a suitable Lyapunov characterization of heterogeneous scalable input-to-state stability (sISS) is proposed. To validate the proposed framework, we consider a nonlinear vehicular platooning scenario, involving both longitudinal and lateral dynamics. In contrast to existing approaches in the time-domain, we show the convenience of the spatial domain in realizing vehicle-following behavior on general curved paths: the spatial domain helps to address the well-known ‘cutting-the-corner’ phenomenon on curved paths. This phenomenon, referring to a platoon progressively cutting the curves of the path, is solved via a delay-based platooning policy, suitably designed in the spatial domain. The proposed spatial-domain platooning protocol guarantees scalable input-to-state stability despite the possible heterogeneity of the vehicle dynamics. Comparative simulations are performed to illustrate the advantages of the proposed approach.