In [1]:
# prob3
# Using GEKKO to solve Optimal Control Problems in MISER Manual (Problem 3)
# 
# we are trying to introduce the use of GEKKO to native MISER user
# this file is prepared by Dr. Joseph Lee
# 
# Dr. H. W. J. Lee
# Department of Applied Mathematics
# The Hong Kong Polytechnic University
In [2]:
# if gekko is not installed, uncomment (delete #) in the following line
#! pip install gekko

# only need to do it once, and put it (#) back as comment once gekko is
# installed, e.g for anaconda python, you only need to do it once to 
# install gekko
#
# however, if you are using Google CoLab to run python, 
# then, you need to install it every time, if so, keep uncomment if you are
# using Google CoLab
In [3]:
# Dodgem Car Problem
# Minimize Final Time

from gekko import GEKKO
import numpy as np
import matplotlib.pyplot as plt
In [4]:
m = GEKKO()
nt = 501
m.time = np.linspace(0,1,nt)

x1 = m.Var(value=np.pi/2.0)
x2 = m.Var(value=4.0)
x3 = m.Var(value=0.0)

p = np.zeros(nt) # final time = 1
p[-1] = 1.0
final = m.Param(value=p)
tf = m.FV(value=1.0,lb=0.1,ub=100.0)
tf.STATUS = 1

u = m.MV(value=0,lb=-2,ub=2)
u.STATUS = 1
m.Equation(x1.dt()==u*tf)
m.Equation(x2.dt()==m.cos(x1)*tf)
m.Equation(x3.dt()==m.sin(x1)*tf)
m.Equation(x2*final<=0)
m.Equation(x3*final<=0)
m.Obj(tf)
m.options.IMODE = 6
In [5]:
m.solve(disp=False)
In [6]:
print('Final Time: ' + str(tf.value[0]))
tm = np.linspace(0,tf.value[0],nt)
plt.figure(figsize=(15,8))
plt.figure(1)
plt.plot(tm,x1.value,'k-',label=r'$x_1$')

plt.plot(tm,x2.value,'b-',label=r'$x_2$')
plt.plot(tm,x3.value,'g--',label=r'$x_3$')
plt.plot(tm,u.value,'r--',label=r'$u$')
plt.legend(loc='best')
plt.xlabel('Time')
plt.legend()
plt.show()

Final Time: 4.3162556133
In [7]:
plt.figure(figsize=(32,4))
plt.plot(x2.value,x3.value)
Out[7]:
[<matplotlib.lines.Line2D at 0x118de5e20>]
In [ ]: