# Game Theory-Based Interactive Control for Human-Machine Cooperative Driving
## 4 Vehicle Interactive Control Strategy
### Interactive Control Based on DMPC and Non-Cooperative Game  
In vehicle interaction, vehicle status information and driving intentions can be shared through the Internet of Vehicles. Both HSCVs and CAVs can predict surrounding vehicles' information in the traffic environment and their own motion status, and this prediction information will be used to update the cost function for vehicle interaction. The autonomous driving controller needs to consider the impact of interactive object information and surrounding environmental risk on itself. For an HSCV, in addition to considering the effects of driver control commands, the shared controller in the HSCV also needs to consider how to interact with surrounding vehicles with different driving styles safely. The status and control strategy of an HSCV (including the driver's control commands and the compensation control commands made by the HSCV automation controller) will affect SVs. Similarly, the status and control strategy of each SV will also affect other traffic participants. In an HSCV, while the automation control system compensates for driver control commands to track the target trajectory, it also needs to consider the safety risks caused by the different driving styles of the SV. The HSCV safety cost function in time step \(k+1\) is expressed as:  
\[J^{e}(k+1)=J^{e}_{s-y}(k+1)+J^{e}_{s-lc}(k+1) \tag{29}\]  
The driving safety cost function of an HSCV in the prediction time domain of \(N_{p}\) is derived as follows:  
\[\mathbf{J}^{e}(k)=\left[ \begin{array}{c}J^{e}(k+1),J^{e}(k+2),\ldots,J^{e}( k+N_{p})\end{array} \right]^{\mathrm{T}} \tag{30}\]  
The motion prediction of SVs is similar to Equation (16) for an HSCV; the only difference is that the SVs' control input is completely determined by the MPC controller in the automation system without the influence of the human driver. Based on the motion prediction information, the driving style cost function of the surrounding vehicle \(V_{i}\) can be predicted at time step \(k+1\):  
\[J^{Vi}(k+1)=(1-k^{Vi})J^{Vi}_{s}(k+1)+k^{Vi}J^{Vi}_{e}(k+1) \tag{31}\]  
The driving style cost function of vehicle \(V_{i}\) in the prediction time domain \(N_{p}\) is derived as follows:  
\[J^{Vi}(k)=\left[ \begin{array}{c}J^{Vi}(k+1),J^{Vi}(k+2),\ldots,J^{Vi}(k+N_{ p})\end{array} \right]^{\mathrm{T}} \tag{32}\]  
SVs with different driving styles will respond differently to the driving behavior of the HSCV while tracking their own trajectory targets. Assume that there are \(m\) adjacent vehicles \(V_{i}=\{V_{1},V_{2},\cdots,V_{m}\}\) around the HSCV that will participate in vehicle interaction. The individual interest of each SV in this non-cooperative game is defined as minimizing the driving style cost function and the error between the vehicle state and its desired state, while the shared controller in the HSCV needs to minimize the driving safety cost function and the error between the vehicle state and the human driver's desired state. The DMPC method is used to solve this problem, and the cost functions of the HSCV and vehicle \(V_{i}\) are derived as follows:\[\min_{\mathbf{u}^{V_{i}}}\Pi^{V_{i}} =\sum_{j=1}^{N_{p}}\
orm{\mathbf{z}^{V_{i}}(k+j)-\mathbf{z}_{ref}^{V_ {i}}(k+j)}_{\mathbf{Q}^{V_{i}}}^{2}+\sum_{j=0}^{N_{c}-1}\
orm{\mathbf{u}^{V_{i}} (k+j)}_{\mathbf{R}^{V_{i}}}^{2}+\sum_{j=1}^{N_{p}}\
orm{I^{V_{i}}(k+j)}_{ \mathbf{P}^{V_{i}}}^{2} \tag{33a}\] \[\min_{\mathbf{u}^{e}}\Pi^{e} =\sum_{j=1}^{N_{p}}\
orm{\mathbf{z}^{e}(k+j)-\mathbf{z}_{ref}^{e} (k+j)}_{\mathbf{Q}^{e}}^{2}+\sum_{j=0}^{N_{c}-1}\
orm{\mathbf{u}^{e}(k+j)}_{ \mathbf{R}^{e}}^{2}+\sum_{j=1}^{N_{p}}\
orm{I^{e}(k+j)}_{\mathbf{P}^{e}}^{2}\] (33b) s.t.