## 2 Nonlinear Feedback Control Analysis of Visual Information in Foggy Section of Expressway
In addition, the driver may be distracted from driving and become nervous, which would finally result in disordered driving behaviors and faulty operations. The nonlinear compensation of visual information [32] consists of physiological photoelectric conversion, visual signal transmission and processing, and other processes. Receiving, transmitting, and processing of visual information is a typical process of information feedback control. The view seen by the driver is input to the eyes in the form of visual information. At this point, the information of people, vehicles, and road conditions on the expressway acts as visual influencing factors on the visual information input to the eyes and is received by the eyes after filtration. The visual receiving and feedback system of nonlinear information disturbances can be abstracted as the basic feedback control model of visual information input to human eyes on the expressway, as shown in Figure 1.  
The driving feedback control equation can be obtained based on the feedback control model from Figure 1.  
\[Y(s)=W(s)E(s)=[F(s)U(s)+V(s)]E(s) \tag{11}\]  
According to Equation (3), the \(Y(s)\) can be obtained through Laplace transform from \(y(t);W(s)\) represents other information input based on the human system; \(V(s)\) represents an arbitrary disturbance caused by the driver for other reasons; \(L(s)\) represents the transfer function of each measuring instrument; and \(C(s)\) represents the transfer function of control factors in fog environment [31]. \[U(s)=C(s)[X(s)-Z(s)]=C(s)[X(s)-L(s)Y(s)] \tag{12}\]  
The Equations (11) and (12) are combined and when eliminated can generate the following:  
\[ \begin{array}{l}Y(s)=W(s)E(s)\\ =\{F(s)C(s)[X_{0}(s)-L(s)Y(s)]+V(s)\}E(s)\\ =\frac{E(s)F(s)C(s)}{1+E(s)F(s)C(s)L(s)}X_{0}(s)+\frac{E(s)}{1+E(s)F(s)C(s)L(s )}V(s)\end{array}  \tag{13}\]Considering that the vehicle is in the process of driving, if the driver's \(i\) visual output is \(Y_{i}(s)\), and there are other \(n\) information inputs based on the human system, then the \(n\) information input can be expressed as \(W_{n}(s)\), and the expansion of Equation (11) can be obtained as follows:  
\[\left\{ \begin{array}{l}Y_{1}(s)=W_{1}(s)E_{11}(s)+W_{2}(s)E_{12}(s)+\cdots+W_{ n}(s)E_{1n}(s)\\ Y_{2}(s)=W_{1}(s)E_{21}(s)+W_{2}(s)E_{22}(s)+\cdots+W_{n}(s)E_{2n}(s)\\ \cdots\cdots\\ Y_{i}(s)=W_{1}(s)E_{i1}(s)+W_{2}(s)E_{i2}(s)+\cdots+W_{n}(s)E_{in}(s)\end{array} \right. \tag{14}\]  
where each \(E_{ij}(s)\) in the formula corresponds to the transfer function of the output \(Y_{k}(s)\) when entering each \(W_{m}(s)\), and the acquisition frequency of \(E_{ij}(s)\) is determined by the  
Figure 1: Basic feedback control model of visual information input in expressway. speed of driving. Equation (14) is decomposed into the transfer function matrix \(E(s)\), which can be constructed as follows:  
\[E(s)=\left( \begin{array}{l}E_{11}(s)E_{12}(s)\cdot\dots\cdot E_{1n}(s)\\ E_{21}(s)E_{22}(s)\cdot\dots\cdot E_{2n}(s)\\ \dots\cdot\\ E_{j1}(s)E_{j2}(s)\cdot\dots\cdot E_{jn}(s)\\ \dots\cdot\\ E_{i1}(s)E_{i2}(s)\cdot\dots\cdot E_{in}(s)\end{array} \right) \tag{15}\]  
During driving, there are more dimensions of information input to the driver than those output from the driver, so the number of input dimensions is greater than that of output dimensions. Namely, if each column of the matrix represents an input dimension and each row represents an output dimension, then \(n>i\). In foggy environments, constantly changing visibility leads to correspondingly changing visual information input to the driver. When there are no obstacles in the front, the driver would constantly adjust driving speed to ensure the visual information input is balanced. This process is achieved by using feedback signals to correct input signals. If there are \(n\)-biased input signals at this time, \(n\) input correction signals will be generated. The input equation of the control system [31] can be expanded to the following:  
\[\left\{