Adaptive Backstepping Control for Vehicular Platoons with Mismatched Disturbances Using Vector String Lyapunov Functions

In this paper, we consider the problem of platooning control with mismatched disturbances using adaptive backstepping method. We aim at simultaneously retaining the compositionality and the robustness of the controller with respect to general types of disturbances. To this end, motivated by the vector Lyapunov function-based analysis, we propose a novel notion called Vector String Lyapunov Function, whose existence implies l
2
weak string stability. Based on this notion, we propose an adaptive backstepping controller for the platoon, where the compositionality and robustness are guaranteed with centralized adaptive laws. Besides, the internal and the l
2
weak string stability are proved under the designed controller. By comparing with an existing method and two different types of disturbances and topologies, we numerically illustrate the effectiveness of the proposed control algorithm.