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

m = GEKKO()

nt = 101
m.time = np.linspace(0,12,nt)

# Parameters
u = m.MV(value=1,ub=1,lb=0)
u.STATUS = 1
u.DCOST = 0

# Variables
x1 = m.Var(value=1)
x2 = m.Var(value=0)

p = np.zeros(nt)
p[-1] = 1.0
final = m.Param(value=p)

# Equations
m.Equation(x1.dt()==u*(10*x2-x1))
m.Equation(x2.dt()==-u*(10*x2-x1)-(1-u)*x2)

# Objective Function
m.Obj(-final*(1-x1-x2))

m.options.IMODE = 6
m.solve()

print('Objective: ' + str(1-x1[-1]-x2[-1]))

plt.figure(1)

plt.subplot(2,1,1)
plt.plot(m.time,x1.value,'k:',lw=2,label=r'$x_1$')
plt.plot(m.time,x2.value,'b-',lw=2,label=r'$x_2$')
plt.ylabel('Value')
plt.legend(loc='best')

plt.subplot(2,1,2)
plt.plot(m.time,u.value,'r-',lw=2,label=r'$u$')
plt.legend(loc='best')
plt.xlabel('Time')
plt.ylabel('Value')

plt.show()