Data and code underlying the arXiv submission: Linear-Quadratic Dynamic Games as Receding-Horizon Variational Inequalities

This data contains simulation results for the automatic power generation control of a 4-zone system, and for a vehicle platooning application., controlled using a receding-horizon approach based on the open-loop Nash equilibrium (ol-NE) and the closed-loop Nash equilibrium (cl-NE) computation<br><strong>Automatic power generation test</strong>The N=4 agents perform a receding-horizon control action based on the computation of a cl-NE for the underlying dynamic game. The test is performed over N_tests=100 randomized initial conditions, and the proposed methodology (with a terminal cost) is compared to a "baseline method", namely, non-cooperative MPC method (without terminal cost). The simulation time T_sim is 100 time-steps. The relative 4_zones_power_system.mat file contains the following data:x_cl: array of size (n_x, 1, T_sim+1, N_tests). It contains the state at each time-step computed using the cl-NE methodu_cl: array of size (n_u, 1, N, T_sim+1, N_tests), where N is the number of agents and n_u is the numbers of input variables for each agent. It contains the input at each time-step computed using the cl-NE methodx_bl: array of size (n_x, 1, T_sim+1, N_tests). It contains the state at each time-step computed using the baseline methodu_bl: array of size (n_u, 1, N, T_sim+1, N_tests), where N is the number of agents and n_u is the numbers of input variables for each agent. It contains the input at each time-step computed using the baseline methodX_f_cl: EllipsoidSet class (see MPT3 toolbox), which cointains the estimated terminal set of the proposed methodnorms_x_0_to_test: vector of dimension 5: for each test, the norm of the initial state is one of the elements, times the radius of X_f_cl<strong>Vehicle platooning test</strong>The N=5 agents perform a receding-horizon control action based on the computation of an ol-NE for the underlying dynamic game. The test is performed over N_tests=1 randomized initial conditions. The simulation time T_sim is 200 time-steps. The relative vehicle_platooning.mat file contains the following data:x_ol: array of size (n_x, 1, T_sim+1, N_tests). It contains the state at each time-step computed using the ol-NE methodu_ol: array of size (n_u, 1, N, T_sim+1, N_tests), where N is the number of agents and n_u is the numbers of input variables for each agent. It contains the input at each time-step computed using the ol-NE method<br><br><br>

本数据集包含两类场景的仿真结果：一是四区域系统自动发电控制场景，二是车辆编队（vehicle platooning）应用场景，两类场景均采用基于开环纳什均衡（open-loop Nash equilibrium, ol-NE）与闭环纳什均衡（closed-loop Nash equilibrium, cl-NE）计算的滚动时域（receding-horizon）方法实施控制。

**自动发电控制测试**
本次测试涉及N=4个智能体，其基于底层动态博弈的cl-NE计算结果执行滚动时域控制动作。本次测试共开展N_tests=100次随机初始条件仿真，并将所提带终端成本的控制方法与“基准方法”——即无终端成本的非合作模型预测控制（model predictive control, MPC）方法——进行对比。仿真总时长T_sim为100个时间步长。配套的`4_zones_power_system.mat`数据文件包含以下内容：
- `x_cl`：维度为`(n_x, 1, T_sim+1, N_tests)`的数组，存储采用cl-NE方法计算得到的各时间步系统状态
- `u_cl`：维度为`(n_u, 1, N, T_sim+1, N_tests)`的数组，其中N为智能体总数量，n_u为单智能体的输入变量数目，存储采用cl-NE方法计算得到的各时间步控制输入
- `x_bl`：维度为`(n_x, 1, T_sim+1, N_tests)`的数组，存储采用基准方法计算得到的各时间步系统状态
- `u_bl`：维度为`(n_u, 1, N, T_sim+1, N_tests)`的数组，其中N为智能体总数量，n_u为单智能体的输入变量数目，存储采用基准方法计算得到的各时间步控制输入
- `X_f_cl`：EllipsoidSet类（详见MPT3工具箱），存储所提方法的估计终端可行域
- `norms_x_0_to_test`：维度为5的向量，对于每一次测试，初始状态的范数等于该向量中的某一元素与X_f_cl半径的乘积

**车辆编队测试**
本次测试涉及N=5个智能体，其基于底层动态博弈的ol-NE计算结果执行滚动时域控制动作。本次测试共开展N_tests=1次随机初始条件仿真。仿真总时长T_sim为200个时间步长。配套的`vehicle_platooning.mat`数据文件包含以下内容：
- `x_ol`：维度为`(n_x, 1, T_sim+1, N_tests)`的数组，存储采用ol-NE方法计算得到的各时间步系统状态
- `u_ol`：维度为`(n_u, 1, N, T_sim+1, N_tests)`的数组，其中N为智能体总数量，n_u为单智能体的输入变量数目，存储采用ol-NE方法计算得到的各时间步控制输入