Residual Learning-Based Control of Vehicle Platoons with $\ell_2$ Stability Guarantees via Recurrent Equilibrium Networks

Brian Delgado; Anh-Tu Nguyen; Hamid Taghavifar

cs.ROSep 27, 2026

Residual Learning-Based Control of Vehicle Platoons with $\ell_2$ Stability Guarantees via Recurrent Equilibrium Networks

Authors: Brian Delgado, Anh-Tu Nguyen, Hamid Taghavifar

Organizations: Concordia University, Montreal, QC, Canada · Research Center LAMIH UMR CNRS 8201, Université Polytechnique Hauts-de-France, and also with INSA Hauts-de-France, Valenciennes, France

Abstract

This paper proposes a residual learning-based control framework for heterogeneous vehicle platoons subject to parametric uncertainty and external disturbances. A nominal controller designed via Linear Matrix Inequalities (LMIs), along with disturbance-observer compensation, is enhanced by a Recurrent Equilibrium Network (REN) trained offline using stored trajectories and nominal-model prediction errors. The REN is constrained to satisfy a prescribed $\ell_2$ -gain bound, enabling sufficient small-gain conditions for local closed-loop stability and disturbance string stability. Experiments demonstrate reduced spacing and velocity errors relative to the nominal controller.

Figures & tables

Fig. 1: Closed loop of the proposed overlapping dynamics, where $\mathcal{C}_{i}$ is the feedback linearization controller.

Fig. 2: Experimental test setup and onboard control architecture.

Parameter	Value	Parameter	Value
$m$	4 kg	$\tau$	0.64 s
$T$	0.02 s	c	0 kg/m
$h$	1 s	$r$	1 m
$\beta$	0.1	$l_{d}$	0.02

TABLE I: Nominal parameters used for controller design.

Performance indicator	Nominal	Proposed
Velocity RMSE follower 1 (m/s)	0.063042	0.042500
Velocity RMSE follower 2 (m/s)	0.056391	0.039722
Spacing RMSE follower 1 (m)	0.216918	0.128285
Spacing RMSE follower 2 (m)	0.135896	0.119276

TABLE II: Experimental performance comparison.

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Lateral String Stability for Vehicle Platoons: Formulation, Definition, and Analysis

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Zachry Department of Civil & Environmental Engineering, Texas A&M University, College Station, TX 77843, USA · J. Mike Walker ’66 Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843, USA

Vehicle Dynamics Lateral String Stability Safety Constraints Fundamental Limits

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Platooning of connected and automated vehicles provides significant benefits in terms of energy efficiency, traffic throughput, and, most critically, safety. These safety benefits depend on string stability, which dictates how disturbances propagate along a vehicle string. Although longitudinal string stability has been extensively examined, lateral string stability, which governs the propagation of path-tracking errors that can lead to unsafe deviations from the desired path, remains underexplored. Its importance is growing as autonomous vehicles increasingly depend on onboard sensing and map-free navigation, where sensor occlusions and tight formations amplify safety risks. This paper presents a framework for lateral string stability that focuses directly on safety-critical, path-relative tracking errors and enables consistent comparison across vehicles that follow the same planned path. The key element of the framework is an arc-length (Eulerian) viewpoint, a departure from traditional analyses, that clarifies how tracking errors at a given point on the path propagate from one vehicle to the next. Building on this foundation, we propose the definition of L2 lateral string stability along with two control strategies: a feedback-feedforward strategy that relies solely on onboard sensing, and a novel learn-from-predecessor strategy that makes use of vehicle-to-vehicle communication. Both strategies are analyzed for lateral string stability with respect to two error measures: tracking error vector and lateral (cross-track) error. Our results show that onboard sensing alone cannot guarantee attenuation of path-tracking errors, imposing a fundamental safety limitation, while V2V communication enables true error attenuation. The analysis further identifies structural controller requirements, showing that nonzero feedback on specific measurements is essential for guaranteeing stability.

Abstract

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