Controller Synthesis for String Stability of Vehicle Platoons

Ploeg, Jeroen; Shukla, Dipan P.; van de Wouw, Nathan; Nijmeijer, Henk · 2014 · OpenAlex-citations

DOI: 10.1109/tits.2013.2291493

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Summary

This paper addresses the challenge of designing controllers for Cooperative Adaptive Cruise Control (CACC) systems that guarantee string stability in vehicle platoons. String stability is critical for safety and performance, as it ensures that disturbances, such as velocity variations from the lead vehicle, attenuate rather than amplify as they propagate down the platoon. While previous methods relied on a posteriori tuning or centralized control, this work develops a systematic controller synthesis method that explicitly incorporates string stability as an a priori design specification. The authors focus on decentralized, ad hoc platooning using $H_\infty$ optimal control, which allows for explicit trade-offs between vehicle-following performance and disturbance attenuation. The methodology begins by formulating the control problem for a homogeneous platoon using a linear cascaded system model. The authors define $L_2$ string stability and derive specific conditions for semi-strict and strict string stability based on the $H_\infty$ norms of transfer functions relating vehicle inputs and outputs. These conditions are then cast into an $H_\infty$ control framework. The controller structure includes feedback and feedforward components, utilizing wireless intervehicle communication with modeled latency. The synthesis approach is applied to two communication topologies: one-vehicle look-ahead (using data from the immediate predecessor) and two-vehicle look-ahead (using data from the two preceding vehicles). The design minimizes the $H_\infty$ norm of the closed-loop system to satisfy the derived string stability conditions while maintaining spacing error convergence. The results demonstrate that the proposed synthesis method successfully generates $L_2$ string-stable controllers for both communication topologies. The analysis reveals that the two-vehicle look-ahead topology is particularly effective at maintaining string stability in the presence of larger communication delays, offering a robust advantage over the simpler one-vehicle scheme. To validate the practical feasibility of the approach, the authors conducted experimental tests using a platoon of three passenger vehicles. The experimental results confirmed that the synthesized controllers achieved the desired string-stable behavior, effectively attenuating disturbances along the vehicle string. The significance of this work lies in providing a rigorous, systematic framework for CACC controller design that guarantees string stability without relying on heuristic tuning. By integrating string stability constraints directly into the $H_\infty$ synthesis process, the method supports scalable, decentralized platooning strategies. The findings highlight the benefits of multi-vehicle look-ahead communication for robustness against communication delays, contributing to the development of safer and more efficient automated driving systems.

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