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

TL;DR

This paper introduces a novel distributed adaptive backstepping control method for vehicular platoons with mismatched disturbances, ensuring stability and robustness through a new vector string Lyapunov function concept.

Contribution

It proposes a new vector string Lyapunov function for stability analysis and develops an adaptive backstepping controller that guarantees string stability and robustness in platooning.

Findings

The proposed controller maintains string stability under disturbances.

Simulation results show improved robustness compared to existing methods.

The method works across different information flow topologies.

Abstract

In this paper, we consider the problem of platooning control with mismatched disturbances using the distributed adaptive backstepping method. The main challenges are: (1) maintaining the compositionality and the distributed nature of the controller, and (2) ensuring the robustness of the controller with respect to general types of disturbances. To address these challenges, we first propose a novel notion that we named "Vector String Lyapunov Function", whose existence implies l2 weak string stability. This notion is based on the vector Lyapunov function-based stability analysis, which depends on the input-to-state-stability of a comparison system. Using this notion, we propose an adaptive backstepping controller for the platoon such that the compositionality and the distributed nature of the controller can be ensured while the internal stability and string stability of the closed-loop system are formally guaranteed. Finally, simulation examples are provided to illustrate the effectiveness of the proposed control algorithm. In particular, we provide simulation results comparing our proposed control algorithm with a recently proposed control algorithm from the literature, under two types of information flow topologies and disturbances.