GEKKO MPC 示例中的默认目标 function

Question

This Model Predictive Control (MPC) example using GEKKO (relating gas pedal movement to car velocity), doesn't explicitly state a cost function to minimize:

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

m = GEKKO()
m.time = np.linspace(0,20,41)

# Parameters
mass = 500
b = m.Param(value=50)
K = m.Param(value=0.8)

# Manipulated variable
p = m.MV(value=0, lb=0, ub=100)
p.STATUS = 1  # allow optimizer to change
p.DCOST = 0.1 # smooth out gas pedal movement
p.DMAX = 20   # slow down change of gas pedal

# Controlled Variable
v = m.CV(value=0)
v.STATUS = 1  # add the SP to the objective
m.options.CV_TYPE = 2 # squared error
v.SP = 40     # set point
v.TR_INIT = 1 # set point trajectory
v.TAU = 5     # time constant of trajectory

# Process model
m.Equation(mass*v.dt() == -v*b + K*b*p)

m.options.IMODE = 6 # control
m.solve(disp=False)

# get additional solution information
import json
with open(m.path+'//results.json') as f:
    results = json.load(f)

plt.figure()
plt.subplot(2,1,1)
plt.plot(m.time,p.value,'b-',label='MV Optimized')
plt.legend()
plt.ylabel('Input')
plt.subplot(2,1,2)
plt.plot(m.time,results['v1.tr'],'k-',label='Reference Trajectory')
plt.plot(m.time,v.value,'r--',label='CV Response')
plt.ylabel('Output')
plt.xlabel('Time')
plt.legend(loc='best')
plt.show()

Can anyone give me an algebraic expression for what cost function GEKKO is minimizing by default for this problem?

Answer 1

With 'CV_TYPE = 2', your cost function is going to be the sum of squared error between setpoint and predicted CV value throughout the horizon length that you defined (m.time).

Please see the below link for detailed equations for squared error form and L1 (CV_TYPE = 1) form of the MPC objective function.

http://apmonitor.com/do/index.php/Main/ControllerObjective

Junho