# Multi-Objective Collaborative Control Method for Multi-Axle Distributed Vehicle Assisted Driving
## 2 Fuzzy Cooperative Control Strategy Based on LTV-MPC
### Fuzzy Collaborative Control Strategy
This can ensure a smooth transition of the weight adjustment coefficient and avoid controller solution oscillation caused by weight mutation. The universe of the assisted driving weight adjustment coefficient at the previous moment \(\lambda_{r,last}\) is \([0,1]\) and the set of fuzzy language values is defined as \(I_{2}\in\{\text{LA}i,\text{MLA}i,\text{MA}i,\text{MHA}i,\text{HA}i\}\),corresponding to low, medium-low, medium, medium-high, and high control. Figure 7b shows the membership function of \(\lambda_{r,last}\). The universe of the assisted driving weight adjustment coefficient \(\lambda_{r}\) is \([0,1]\). The set of fuzzy language values is defined as \(O_{1}\in\{\text{LAo},\text{MLAo},\text{MAo},\text{MHAo},\text{HAo}\}\), which also correspond to different levels of control permissions (low, medium-low, medium, medium-high, high) of the intelligent assisted driving system. The specific membership function design of the output is shown in Figure 7c, and the specific definition of human-machine collaboration fuzzy rules is shown in Table 1. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{_CI_} & \multicolumn{6}{c}{\(\lambda_{r,last}\)} \\ \cline{2-6}  & **LA\(i\)** & **MLA\(i\)** & **MA\(i\)** & **MA\(i\)** & **MA\(i\)** & **HA\(i\)** \\ \hline LC & LAo & LAo & MLAo & MLAo & MAo \\ MLC & LAo & MLAo & MLAo & MAo & MAo \\ MC & MLAo & MLAo & MAo & MAo & MHAo \\ MHC & MLAo & MAo & MHAo & MHAo & MHAo \\ HC & MLAo & MAo & MHAo & MHAo & HAo \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Human–machine collaborative fuzzy rule library. Figure 7: The specific membership function design. (**a**) Membership function of \(CI\). (**b**) Membership function of \(\lambda_{r,last}\). (**c**) Membership function of \(\lambda_{r}\). (2) **Collaborative fuzzy strategy for handling stability**  
Based on the analysis of the stable state of the vehicle, the stable state, transitional state, and unstable state of the vehicle are defined according to the steering angle \(\delta_{1}\) under different operating conditions. In addition, the driving process of the vehicle is transient, so based on this, the real-time state of the vehicle is evaluated by combining the angle change rate \(\dot{\delta}_{1}\). When the angle change rate is greater, the vehicle is more likely to lose stability. The universe of \(\delta_{1}\) is based on the range of steering angle constraints \([\delta_{1,min},\delta_{1,max}]\) and the set of fuzzy language values are defined as \(I_{3}\in\{\text{NL},\text{NS},\text{ZO},\text{PS},\text{PL}\}\), corresponding to negative large, negative small, zero, positive small, and positive large, respectively. A road adhesion coefficient of 0.8 and a vehicle speed of 20 m/s are used as the nominal operating conditions, and the critical steering angles \(\pm\delta_{1,N}\) and \(\pm\delta_{1c,N}\) are combined to divide the interval for membership function design, as shown in Figure 8a. For other operating conditions, the steering angle can be mapped to the nominal operating condition based on the obtained calibrated criteria angle data and the principle of proportionality. \(\dot{\delta}_{1}\) is the angle change rate, which represents the change of the steering angle per unit time. Its universe is \(\left[\dot{\delta}_{1,min},\dot{\delta}_{1 max}\right]\). Based on the same nominal operating conditions, two critical angle change rates are set as \(\pm\dot{\delta}_{1,N}\) and \(\pm\dot{\delta}_{1,N}\), defined in the fuzzy language set as \(I_{4}\in\{\text{NL},\text{NS},\text{ZO},\text{PS},\text{PL}\}\), and the membership function design is shown in Figure 8b. The universe of output variable \(\lambda_{\beta}\) is \([0,1]\), and the fuzzy language set is \(O_{2}\in\{\text{LSC},\text{MLSC},\text{MSC},\text{MHSC},\text{HSC}\}\), corresponding to low, medium-low, medium, medium-high, and high stability control, respectively. The membership function design is shown in Figure 8c.