# Stability Analysis of Lane-Keeping Assistance System for Trucks under Crosswind Conditions
## 1 Introduction  
When vehicles are subjected to crosswinds during high-speed travel, their lateral positions can deviate, and this is especially true for box-shaped vehicles such as vans, large buses, and canvas-covered trucks. This deviation negatively affects the stability of vehicle handling, potentially leading to accidents. Addressing the issue of crosswind disturbances in high-speed vehicle operation is an important aspect of research on vehicle handling stability, and significant research has been conducted in this area. [PERSON] and [PERSON] [1] used Monte Carlo simulations to assess the impact of ambient wind on vehicle performance and emissions. [PERSON] et al. [2] proposed a pure pursuit path-tracking method based on an eight-degrees-of-freedom model to address the influence of wind loads and floating bridge movements on the lateral stability of public buses in Bjernafjord, Norway. [PERSON] et al. [3] developed a coupled vibration analysis of the wind, vehicle, and bridge to ensure the safety of vehicles on long-span bridges under crosswind conditions. [PERSON] and [PERSON] [4] analyzed the problems of a vehicle-rail coupled system as a stochastic nonlinear system under the excitations of crosswind and random track irregularities. They proposed a stochastic analysis model for vehicle-rail coupling dynamics and random irregularities. [PERSON] et al. [5] introduced a lateral disturbance compensation algorithm to reduce the driver steering effort under crosswind disturbances. [PERSON] et al. [6] used a dynamic driving simulator to evaluate a driver's state when encountering crosswind and found that the driver's response typically exhibits an approximate delay of 0.25 s from the onset of crosswind stimuli. [PERSON] et al. [7] developed a comprehensive evaluation framework for the lateral stability of vehicles under crosswind conditions, which provides guidancefor controlling adverse conditions and making road maintenance decisions. Although these methods have performed well in practical applications, the accuracy of their lateral deviation control is limited due to the lack of consideration of the influence of the vehicle's sideslip angle. In modern society, traffic accidents continually occur, leading to increasing casualties. Surveys have shown that approximately 50% of traffic accidents are caused by vehicles deviating from their normal travel lane. To address the issue of vehicles unintentionally deviating from their intended travel path, researchers have begun to study the control strategies of lane-keeping assistance systems (LKASs). [PERSON] et al. [8] proposed an advanced LKAS with two switchable auxiliary modes, namely the lane departure prevention and co-driver lane-keeping modes, to address the reliability issues of fully autonomous lane-keeping systems. [PERSON] et al. [9] presented a torque overlay-based robust steering wheel angle control method for the lane-keeping systems of autonomous vehicles. [PERSON] et al. [10] suggested a lane-keeping control method based on a Takagi-Sugeno fuzzy model to reduce the lateral deviation of vehicles. [PERSON] et al. [11] proposed a deep learning model to estimate the lateral distance between a vehicle and the lane boundary, providing an effective benchmark for road testing of LKASs. [PERSON] et al. [12] developed a driver-centric and neural-adaptive control-based LKAS to address traffic safety issues caused by vehicle departures from lanes. [PERSON] et al. [13] developed a novel lane-keeping assistance method that applies additional yaw moments to electric vehicles and actively distributes the driving/braking torque to all four wheels for lane keeping. [PERSON] et al. [14] addressed the frequent lane departure issue in commercial vehicles and devised an LKAS based on an electro-hydraulic steering system. [PERSON] et al. [15] designed an LKAS based on human driving data to prevent vehicle lane departures in situations with an unaware driver. [PERSON] et al.