## 2 Nonlinear Feedback Control Analysis of Visual Information in Foggy Section of Expressway  
The preliminary research has studied the impact of the road design elements (road alignment, road space, and climate environment) on drivers' driving behaviors, and thus it is a passive analysis of the potential risks of adverse factors like climate linearity to driving safety. In view of the impact of global air pollution, urban heat islands and wet islands on the current climate, the influence of haze and dense winter fog, especially agglomerate fog, on expressway traffic safety is increasingly severe [27]. Speed limits, road closures, and large-scale and super-large-scale traffic accidents caused by low-visibility climates such as fog, agglomerate fog, and haze happen occasionally, which have a serious impact on road use efficiency and result in great losses of life and property. When determining design speeds for roads, road designers often do not take much account of the influence of sudden climate disasters such as agglomerate fog but perform this work based on road traffic environments under ideal climate conditions. Therefore, it can be preliminarily assumed that, without considering traffic flow conditions, the balance state of the expressway driving system proposed by the road designer can be achieved when the driver has a good visual physiological state and drives the vehicle within the design speed range in good weather. However, after the vehicle enters a low-visibility agglomerate fog section, the amount of visual information received by human eyes will reduce with the decrease in visibility [28]. Meanwhile, the fog acts on the road surface and further on the vehicle and driver through changes in the friction coefficient of the road surface and the mirror surface effect, finally causing disturbances to the speeds of the traffic flow and the vehicle. Changes in vehicle speed will react upon the driver's visual acuity, thus leading to an imbalance of the human visual decision-feedback system. In the field of communications, signals are divided into digital signals and analog signals. Analog signals are continuous waveform signals, while digital signals are discrete signals, such as computer signals. Digital signals are more conducive to the calculation of visual information received by the driver during driving. According to the Shannon theorem [29], the visual information received by human eyes during communication can be converted to codes. Therefore, by expressing physical information in mathematical form, the information communication process can be transformed into a mathematical operation process [30]. When the vehicle initially enters an agglomerate fog road section, the view of the road section in the visual field of human eyes can be seen as a circular light curtain vertically, and digital codes can be used to represent visual information. In this way, the light curtain diagram of visual information received by human eyes during driving in the agglomerate fog road section can be obtained. The diameter of the field of regard is used as the research parameter in this paper. Thus, the below-mentioned field of regard is expressed by the width of the field. In the initial emergency braking phase, the diameter of the field of regard is the minimum, and the least amount of road information is received. The control theory is used to analyze the input and output of human eye information process [31]. We set the difference between input \(x(t)\) and output \(y_{i}(t)\) as \(e(t)\), calculated as follows:  
\[e(t)=x(t)-y_{i}(t)=e^{-t/\tau_{1}} \tag{1}\]  
\[x=\tau_{1}\frac{dy}{dt}+y \tag{2}\]  
Visualizing the information input and output from the driver in foggy environments can be described by a first-order system, which can be approximately abstracted as the input-output control system model. The problem can be normalized through Laplace transform.