Stability analysis and controller design of the Cooperative Adaptive Cruise Control platoon considering a rate-free time-varying communication delay and uncertainties

In recent years, Cooperative Adaptive Cruise Controls (CACCs) have been increasingly studied as a promising solution to problems such as traffic congestion and pollutant emissions. Despite their potential, the communication delays within CACC systems undermine the effectiveness of regular feedback control method in guaranteeing the fundamental control objective of stability. Considerable research has been conducted to derive stability conditions that account for communication delays. However, the time-varying and rate-free attributes of communication delay make deriving stability conditions highly challenging. To address this, this paper proposes a novel stability condition for the CACC platoon considering a rate-free communication delay using the Lyapunov–Krasovskii Stability Theorem and Schur complement. Additionally, we deduce a robust stability condition that takes into account measure uncertainties. Building on these foundations, a centralized $H_{\infty }$ controller is developed to address rate-free disturbances, ensuring string stability. Furthermore, extensive numerical analyses are conducted to investigate the impact of a rate-free communication delay and measurement uncertainties on tracking performance, transient response, and safety conditions. The results demonstrate that CACCs can effectively track errors and achieve equilibrium if the stability condition is met. Realistic scenarios incorporating rate-free communication delays and measurement uncertainties are associated with diminished tracking performance, transient responses, and safety conditions when compared to ideal scenarios characterized by constant communication delays. Furthermore, the $H_{\infty }$ controller surpasses the regular controller in tracking performance and maintains string stability amidst rate-free communication delays. Specifically, under the $H_{\infty }$ controller, the peak spacing error is reduced to merely 83.68% of that observed with the regular controller. The deployment of the $H_{\infty }$ controller facilitates a significant reduction in settling time (ST) by 90.04% and effectively prevents overshoot, thereby ensuring string stability, in stark contrast to the regular controller, which only achieves a 79.34% reduction in ST and a 5.97% reduction in maximum overshoot. Moreover, the $H_{\infty }$ controller markedly reduces the likelihood of high-risk scenarios in comparison to the regular controller. Moreover, CACCs with access to more distant and abundant information demonstrate superior transient response and safety conditions.