提供代码：三车协同自适应巡航(CACC)实现编队控制

以下是基于 Python 和 MATLAB 的三车协同自适应巡航(CACC)实现编队控制的代码示例：

Python 代码：

import numpy as np
from scipy.integrate import odeint
import matplotlib.pyplot as plt

# 车辆参数
m = 1000  # 质量
c = 40  # 阻尼系数
k = 2000  # 弹簧刚度
v_des = 20  # 设定速度

# 控制器参数
a1 = 1
a2 = 1
a3 = 1
a4 = 1

# 初始状态
x0 = [0, 0, 0, 0, 0, 0, 0, 0, 0]

# 时间间隔和仿真时间
dt = 0.01
t = np.arange(0, 10, dt)

# 控制输入
u = np.zeros((3, len(t)))

# 定义车辆动力学模型
def vehicle_model(x, t, u, m, c, k):
    x1, x2, x3, x4, x5, x6, x7, x8, x9 = x
    u1, u2, u3 = u
    x1_dot = x2
    x2_dot = (u1 - c * x2 - k * x1 - a1 * (x2 - x5) + a2 * (x5 - x2) + a3 * (x5 - x8) - a4 * (x8 - x2)) / m
    x3_dot = x4
    x4_dot = (u2 - c * x4 - k * x3 - a1 * (x4 - x6) + a2 * (x6 - x4) + a3 * (x6 - x9) - a4 * (x9 - x4)) / m
    x5_dot = x6
    x6_dot = (v_des - x5 - c * (x6 - x2) - k * (x5 - x1) - a1 * (x6 - x9) + a2 * (x9 - x6) + a3 * (x9 - x4) - a4 * (x4 - x6)) / m
    x7_dot = x8
    x8_dot = (u3 - c * x8 - k * x7 - a1 * (x8 - x9) + a2 * (x9 - x8) + a3 * (x9 - x6) - a4 * (x6 - x8)) / m
    x9_dot = x9
    return [x1_dot, x2_dot, x3_dot, x4_dot, x5_dot, x6_dot, x7_dot, x8_dot, x9_dot]

# 仿真过程
for i in range(len(t)-1):
    # 控制输入计算
    u[0,i+1] = -a1 * (x0[1,i] - x0[4,i]) + a2 * (x0[4,i] - x0[1,i]) + a3 * (x0[4,i] - x0[7,i]) - a4 * (x0[7,i] - x0[1,i])
    u[1,i+1] = -a1 * (x0[3,i] - x0[5,i]) + a2 * (x0[5,i] - x0[3,i]) + a3 * (x0[5,i] - x0[8,i]) - a4 * (x0[8,i] - x0[3,i])
    u[2,i+1] = -a1 * (x0[7,i] - x0[8,i]) + a2 * (x0[8,i] - x0[7,i]) + a3 * (x0[8,i] - x0[5,i]) - a4 * (x0[5,i] - x0[8,i])
    # 车辆动力学方程求解
    x = odeint(vehicle_model, x0[:,i], [t[i], t[i+1]], args=(u[:,i+1], m, c, k))
    x0[:,i+1] = x[-1,:]

# 画图
plt.figure()
plt.plot(t, x0[0,:], label='Car 1')
plt.plot(t, x0[2,:], label='Car 2')
plt.plot(t, x0[6,:], label='Car 3')
plt.xlabel('Time (s)')
plt.ylabel('Position (m)')
plt.legend()
plt.show()

MATLAB 代码：

% 车辆参数
m = 1000;  % 质量
c = 40;  % 阻尼系数
k = 2000;  % 弹簧刚度
v_des = 20;  % 设定速度

% 控制器参数
a1 = 1;
a2 = 1;
a3 = 1;
a4 = 1;

% 初始状态
x0 = [0, 0, 0, 0, 0, 0, 0, 0, 0];

% 时间间隔和仿真时间
dt = 0.01;
t = 0:dt:10;

% 控制输入
u = zeros(3, length(t));

% 定义车辆动力学模型
function x_dot = vehicle_model(t, x, u, m, c, k, a1, a2, a3, a4, v_des)
    x1 = x(1);
    x2 = x(2);
    x3 = x(3);
    x4 = x(4);
    x5 = x(5);
    x6 = x(6);
    x7 = x(7);
    x8 = x(8);
    x9 = x(9);
    u1 = u(1);
    u2 = u(2);
    u3 = u(3);
    x1_dot = x2;
    x2_dot = (u1 - c * x2 - k * x1 - a1 * (x2 - x5) + a2 * (x5 - x2) + a3 * (x5 - x8) - a4 * (x8 - x2)) / m;
    x3_dot = x4;
    x4_dot = (u2 - c * x4 - k * x3 - a1 * (x4 - x6) + a2 * (x6 - x4) + a3 * (x6 - x9) - a4 * (x9 - x4)) / m;
    x5_dot = x6;
    x6_dot = (v_des - x5 - c * (x6 - x2) - k * (x5 - x1) - a1 * (x6 - x9) + a2 * (x9 - x6) + a3 * (x9 - x4) - a4 * (x4 - x6)) / m;
    x7_dot = x8;
    x8_dot = (u3 - c * x8 - k * x7 - a1 * (x8 - x9) + a2 * (x9 - x8) + a3 * (x9 - x6) - a4 * (x6 - x8)) / m;
    x9_dot = 0;
    x_dot = [x1_dot; x2_dot; x3_dot; x4_dot; x5_dot; x6_dot; x7_dot; x8_dot; x9_dot];
end

% 仿真过程
for i = 1:length(t)-1
    % 控制输入计算
    u(1,i+1) = -a1 * (x0(2,i) - x0(5,i)) + a2 * (x0(5,i) - x0(2,i)) + a3 * (x0(5,i) - x0(8,i)) - a4 * (x0(8,i) - x0(2,i));
    u(2,i+1) = -a1 * (x0(4,i) - x0(6,i)) + a2 * (x0(6,i) - x0(4,i)) + a3 * (x0(6,i) - x0(9,i)) - a4 * (x0(9,i) - x0(4,i));
    u(3,i+1) = -a1 * (x0(8,i) - x0(9,i)) + a2 * (x0(9,i) - x0(8,i)) + a3 * (x0(9,i) - x0(6,i)) - a4 * (x0(6,i) - x0(9,i));
    % 车辆动力学方程求解
    [t_, x] = ode45(@(t, x) vehicle_model(t, x, u(:,i+1), m, c, k, a1, a2, a3, a4, v_des), [t(i), t(i+1)], x0(:,i));
    x0(:,i+1) = x(end,:)';
end

% 画图
figure
plot(t, x0(1,:), 'r', t, x0(3,:), 'g', t, x0(7,:), 'b')
xlabel('Time (s)')
ylabel('Position (m)')
legend('Car 1', 'Car 2', 'Car 3')

这个示例代码演示了三辆汽车的自适应控制，以实现编队控制。控制器使用了经典的 CACC 控制策略，包括了位置和速度误差的反馈和前馈控制。在仿真过程中，车辆动力学方程使用了 ODE 求解器进行求解，并且使用了 MATLAB 和 Python 两种编程语言实现。