On the Constrained CAV Platoon Control Problem

TL;DR

This work tackles constrained CAV platoon control in mixed traffic by enforcing explicit lower/upper bounds on controller gains and mitigating delay effects. It introduces a parameterized, box-constrained framework for locally stabilizing gains, and employs a Padé-approximation to reliably enforce string stability in the presence of time delays, outperforming Taylor-based methods especially at larger delays. A two-stage near-optimal procedure—first obtaining a feasible stabilizing point, then refining the gains to minimize the delay-robust H∞ metric over predominant acceleration frequencies—yields controllers that effectively attenuate stop-and-go disturbances in mixed platoons. The approach demonstrates improved disturbance attenuation and stability in simulations, suggesting practical potential for reducing collisions in modern transportation systems, while acknowledging limitations and directions for robust and data-driven enhancements.

Abstract

The main objective of the connected and automated vehicle (CAV) platoon control problem is to regulate CAVs' position while ensuring stability and accounting for vehicle dynamics. Although this problem has been studied in the literature, existing research has some limitations. This paper presents two new theoretical results that address these limitations: (i) the synthesis of unrealistic high-gain control parameters due to the lack of a systematic way to incorporate the lower and upper bounds on the control parameters, and (ii) the performance sensitivity to the communication delay due to inaccurate Taylor series approximation. To be more precise, taking advantage of the wellknown Pade approximation, this paper proposes a constrained CAV platoon controller synthesis that (i) systematically incorporates the lower and upper bounds on the control parameters, and (ii) significantly improves the performance sensitivity to the communication delay. The effectiveness of the presented results is verified through conducting extensive numerical simulations. The proposed controller effectively attenuates the stop-and-go disturbance -- a single cycle of deceleration followed by acceleration -- amplification throughout the mixed platoon (consisting of CAVs and human-driven vehicles). Modern transportation systems will benefit from the proposed CAV controls in terms of effective disturbance attenuation as it will potentially reduce collisions.

Figures (4)

• Figure 1: The $\omega$-dependent $|F(j\omega)|$ values corresponding to the unconstrained and constrained $\mathcal{H}_{\infty}$ syntheses $k^{\mathrm{unc}}$ and $k^{\ast}$ with $\theta = 0.1$ and $\omega_1 = 0.5$ for $\omega \in [\omega_1,\omega_2]$ on the left and $\omega \in [0.01,5.01]$ on the right.
• Figure 2: The relative error percentages $100 \times \frac{|F(j\omega)|-|\hat{F}(j\omega)|}{|F(j\omega)|}$ (%) associated with the Taylor series approximation-based method and the Padé approximation-based method with $\theta = 0.1$ and $\omega_1 = 0.5$ for $\omega \in [\omega_1,\omega_2]$ on the left and $\omega \in [0.01,5.01]$ on the right.
• Figure 3: The $3$D search space (fixing $\kappa_3 = \kappa_3^{\ast}$ and $\kappa_4 = \kappa_4^{\ast}$) corresponding to the constrained $\mathcal{H}_{\infty}$ controller synthesis $k^{\ast}$ with $\theta = 0.1$ and $\omega_1 = 0.5$.
• Figure 4: The $\omega$-dependent $|F(j\omega)|$ values corresponding to the constrained $\mathcal{H}_{\infty}$ controller synthesis $k^{\ast}$ for $\omega \in [\omega_1,\omega_2]$ on the left and $\omega \in [0.01,5.01]$ on the right.

Theorems & Definitions (11)

• Definition 1: Local stability li2018robustzhou2020stabilizing
• Definition 2: Strict string stability naus2010stringzhou2020stabilizing
• Proposition 1
• Corollary 1
• Lemma 1
• Proposition 2
• Corollary 2
• Corollary 3
• Remark 1
• Remark 2