Python 解决 GEKKO 中的后退地平线控制

我试图在Python中使用GEKKO实现一个后退地平线控制(RHC)方案，我想判断一下我的公式.目标是在一定范围内求解从t=tk到t=tk+H-1的OCP，在tk处应用控制解，并丢弃剩余值(u\u k+1到u\u k+H-1).下面的代码似乎给出了正确的解决方案，但我想验证我在GEKKO中使用了正确的函数，即在"重置"下一个视界的状态时.我在try 使用.VALUE功能重置x1和x2时遇到了一些问题，例如TypeError: 'float' object is not subscriptable.

import numpy as np
import matplotlib.pylab as plt
from gekko import GEKKO

if __name__ == '__main__':

    # Instantiate GEKKO
    m = GEKKO()

    # Constants
    nRHC = 21
    tRHC = 2
    m.time = np.linspace(0, tRHC, nRHC)

    # Control
    u = m.MV(value=0.0,fixed_initial=False)
    u.STATUS = 1 
    u.DCOST = 0

    # Vars
    t = m.SV(value=0)
    x1 = m.SV(value=1)
    x2 = m.SV(value=0)

    # Equations
    m.Equation(t.dt() == 1)
    m.Equation(x1.dt() == x2)
    m.Equation(x2.dt() == (1 - x2*x2)*x1 - x2 + u)

    # Objective Function
    m.Minimize(10*x1**2 + 10*x2**2 + u**2)

    # Solve RHC
    m.options.IMODE = 6
    m.options.NODES = 11
    m.options.MV_TYPE = 2
    m.options.SOLVER = 3
    nTotal = 101
    tTotal = np.linspace(0, 10, nTotal)
    uStore = np.zeros((1,nTotal))
    xStore = np.zeros((2,nTotal))
    xStore[:,0] = [1, 0]
    for i in range(nTotal):
        print('Solving Step: ', i+1, ' of ', nTotal-1)
        if i == nTotal-1:
            break

        # Solve MPC over horizon
        m.solve(disp=False)

        # Update States
        t.VALUE = t[1]
        x1.MEAS = x1[1]
        x2.MEAS = x2[1]
        
        # Store
        uStore[:,i] = u.NEWVAL
        xStore[:,i+1] = np.array([x1[1], x2[1]])

    # Plot States
    f1, axs = plt.subplots(2)    
    axs[0].plot(tTotal, xStore[0,:])
    axs[0].set_ylabel('x')
    axs[0].grid()
    axs[1].plot(tTotal, xStore[1,:])
    axs[1].set_ylabel('x_dot')
    axs[1].set_xlabel('time')
    axs[1].grid()

    # Show Plots
    plt.show()

非常感谢.