Time optimal car problem (GEKKO) - Revision history

JohnHedengren: Update with latest Gekko v1.0.5

2022-08-28T13:23:10Z

Update with latest Gekko v1.0.5

← Older revision		Revision as of 13:23, 28 August 2022
Line 15:		Line 15:
	Z1 = m.Var(value=0, ub=330, lb=0)		Z1 = m.Var(value=0, ub=330, lb=0)
	Z2 = m.Var(value=0, ub=33, lb=0)		Z2 = m.Var(value=0, ub=33, lb=0)
	m.~~fix~~(Z2~~, len(m.time)-1~~, 0)		m.fix_final(Z2, 0)
	m.~~fix~~(Z1~~, len(m.time)-1~~, 300)		m.fix_final(Z1, 300)

	# set up the value we modify over the horizon		# set up the value we modify over the horizon

JohnHedengren at 19:42, 13 March 2019

2019-03-13T19:42:41Z

← Older revision		Revision as of 19:42, 13 March 2019
Line 60:		Line 60:
	== Results with APOPT (MINLP) ==		== Results with APOPT (MINLP) ==

	An MINLP solution is calculated with APOPT with an objective function value of <math>30.3077</math>.		An MINLP solution is calculated with APOPT with an objective function value of <math>30.3077</math>. Thanks to [https://www.linkedin.com/in/tjasperson/ Tanner Jasperson] for providing a solution.

	[[File:Time_optimal_car_GEKKO.png]]		[[File:Time_optimal_car_GEKKO.png]]

	[[Category:Gekko]]		[[Category:Gekko]]

JohnHedengren: Create results page with Python GEKKO

2019-03-13T19:36:27Z

Create results page with Python GEKKO

New page

This page contains a solution of the [[Time optimal car problem]] in [https://gekko.readthedocs.io/en/latest/ GEKKO] Python format. The GEKKO package is available with '''pip install gekko'''. The Python code uses orthogonal collocation and a simultaneous optimization method. The end point constraints are imposed as hard constraints.

<source lang="Python">
from gekko import GEKKO
import matplotlib.pyplot as plt
import numpy as np

# set up the gekko model
m = GEKKO()

# set up the time (minimize the time with time scaling)
m.time = np.linspace(0, 1, 100)

# set up the variables
Z1 = m.Var(value=0, ub=330, lb=0)
Z2 = m.Var(value=0, ub=33, lb=0)
m.fix(Z2, len(m.time)-1, 0)
m.fix(Z1, len(m.time)-1, 300)

# set up the value we modify over the horizon
tf = m.FV(value=500, lb=0.1)
tf.STATUS = 1

# set up the MV
u = m.MV(integer=True, lb=-2, ub=1)
u.STATUS = 1

# set up the equations
m.Equation(Z1.dt() / tf == Z2)
m.Equation(Z2.dt() / tf == u)

# set the objective
m.Obj(tf)

# set up the options
m.options.IMODE = 6
m.options.SOLVER = 1

# solve
m.solve(disp=False)

# print the time
print("Total time taken: " + str(tf.NEWVAL))

# plot the results
plt.figure()
plt.subplot(211)
plt.plot(np.linspace(0,1,100)*tf.NEWVAL, Z1, label=r'$Z_1$')
plt.plot(np.linspace(0,1,100)*tf.NEWVAL, Z2, label=r'$Z_2$')
plt.ylabel('Z')
plt.legend()
plt.subplot(212)
plt.plot(np.linspace(0,1,100)*tf.NEWVAL, u, label=r'$u$')
plt.ylabel('u')
plt.xlabel('Time')
plt.legend()
plt.show()
</source>

== Results with APOPT (MINLP) ==

An MINLP solution is calculated with APOPT with an objective function value of <math>30.3077</math>.

[[File:Time_optimal_car_GEKKO.png]]

[[Category:Gekko]]