pyProject/deepc_test.py

import numpy as np
from scipy.optimize import minimize

# 系统参数
A = 0.8
B = 0.5
C = 1
D = 0.2

# 参考轨迹函数
def reference_trajectory(t):
    return np.sin(0.1 * t)

# 生成输入数据
def generate_input_data(T):
    return np.random.uniform(-1, 1, T)

# 系统模拟
def simulate_system(u):
    x = 0  # 初始状态
    y = []
    for i in range(len(u)):
        x = A * x + B * u[i]
        y.append(C * x + D * u[i])
    return np.array(y)

# DeePC算法实现
def deepc_algorithm(T, Tini, N):
    # 生成输入数据
    ud = generate_input_data(T)

    # 模拟系统得到输出数据
    yd = simulate_system(ud)

    # 划分数据
    Up, Yp, Uf, Yf = partition_data(ud, yd, Tini, N)

    # 构建优化问题
    def objective_function(g):
        u = Uf @ g
        y = Yf @ g
        cost = np.sum((y - reference_trajectory(np.arange(Tini, Tini + N))) ** 2) + 0.1 * np.sum(u ** 2)
        return cost

    # 等式约束
    def equality_constraint(g):
        return np.concatenate((Up @ g - ud[:Tini], Yp @ g - yd[:Tini], Uf @ g, Yf @ g))

    # 初始猜测
    g0 = np.zeros((T - Tini - N + 1, 1))

    # 约束条件
    constraints = {'type': 'eq', 'fun': equality_constraint}

    # 求解优化问题
    result = minimize(objective_function, g0, constraints=constraints)

    # 最优输入序列
    u_opt = Uf @ result.x

    return u_opt

# 划分数据函数
def partition_data(ud, yd, Tini, N):
    Up = np.zeros((Tini, T - Tini - N + 1))
    Yp = np.zeros((Tini, T - Tini - N + 1))
    Uf = np.zeros((N, T - Tini - N + 1))
    Yf = np.zeros((N, T - Tini - N + 1))

    for i in range(T - Tini - N + 1):
        Up[:, i] = ud[i:i + Tini]
        Yp[:, i] = yd[i:i + Tini]
        Uf[:, i] = ud[i + Tini:i + Tini + N]
        Yf[:, i] = yd[i + Tini:i + Tini + N]

    return Up, Yp, Uf, Yf

# 测试
T = 100
Tini = 10
N = 5
u_opt = deepc_algorithm(T, Tini, N)
print(u_opt)