Использование зависимой от переменной функции в ограничениях - PullRequest
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Использование зависимой от переменной функции в ограничениях

2 голосов
/ 10 июля 2020

Я пытаюсь оптимизировать следующую проблему с помощью gekko: enter image description here

The problem is that the dynamics of the problem contain a term, kappa, that is dependent on s but the only relationship I am provided between them are data of kappa at every discrete points in s.

I'm also trying to formulate my problem in both discrete and continuous form to see which one runs faster. My attempt is to estimate kappa as a function of s using cspline but I'm having errors implementing it to the constraints in both. You can see the code below:

In discrete time:

now = time.time()
p = GEKKO(remote=False)

sg = []
rhog = []
thetag = []
betag = []
vg = []
ag = []
curvg = [] #kappa

#parameters
T = p.Const(value=0.5)
vref = p.Const(value=3)
nT = 11

#kappa and s reference
arcref = refpath[2,minid:]-refpath[2,minid]
curvref = refpath[3,minid:]

for i in range(nT):
    #Set variables
    sg.append(p.Var(value = sinit))
    rhog.append(p.Var(value = rhoinit))
    thetag.append(p.Var(value = 0))
    betag.append(p.Var(value = 0))
    vg.append(p.Var(value = 0))
    ag.append(p.Var(value = 0))
    curvg.append(p.Var())
    
    #Set objective function
    p.Obj(rhog[i]**2 + (vg[i]- vref)**2 + ag[i]**2)
    
    #Estimate kappa
    p.cspline(sg[i], curvg[i], arcref, curvref)

for i in range(nT-1):
    #Set constraints
    p.Equation( vg[i+1] == vg[i] + T*ag[i] )
    p.Equation( sg[i+1] == sg[i] + T*vg[i]*p.sin(thetag[i]) )
    p.Equation( rhog[i+1] == rhog[i] + T*vg[i]*p.cos(thetag[i])/(1-rhog[i]*curvg) )
    p.Equation( thetag[i+1]-betag[i+1]+curvg[i+1]*sg[i+1] == thetag[i]-betag[i]+curvg[i]*sg[i] )

p.options.IMODE = 3
p.options.SOLVER = 3
p.options.WEB = 0

p.solve(disp=False, debug=True)
print(f'run time: {time.time()-now}')

, и я получил ошибку 

Exception: @error: Model Expression
 *** Error in syntax of function string: Missing operator

Position: 2                   
 0,0,0,0,0,0,0,0,0,0,0
  ?

В непрерывном режиме: 

now = time.time()
p = GEKKO(remote=False)

#Set variables
sg = p.Var(value=sinit)
rhog = p.Var(value=rhoinit)
vg = p.Var(value=0)
ag = p.Var(value=0)
thetag = p.Var(value=0)
betag = p.Var(value=0)

curvg = p.Var()
#Parameters
T = 0.5
vref = p.Const(value=3)
nT = 11

#kappa and s reference
arcref = refpath[2,minid:]-refpath[2,minid]
curvref = refpath[3,minid:]

p.time = np.linspace(0,nT,nT*2)

p.options.IMODE = 6
p.options.SOLVER = 3
p.options.WEB = 0

p.Obj( rhog**2 + (vg - vref)**2 + ag**2 )

#set kappa estimate
p.cspline(sg, curvg, arcref, curvref)

p.Equation(sg.dt()==vg*p.cos(thetag)/(1-rhog*curvg))
p.Equation(rhog.dt()==vg*p.sin(thetag))
p.Equation(vg.dt()==ag)
p.Equation(thetag.dt()==betag.dt()-curvg*sg.dt())

p.solve(disp=False, debug=True)
print(f'run time: {time.time()-now}')

и я получил ошибку: 

Error: free(): invalid size

Program received signal SIGABRT: Process abort signal.

Backtrace for this error:
#0  0x6c278f
#1  0x6aacd0
#2  0x7f95ba478fcf
#3  0x7f95ba478f47
#4  0x7f95ba47a8b0
#5  0x7f95ba4c3906
#6  0x7f95ba4ca979
#7  0x7f95ba4d1e9b
#8  0x4f54a6
#9  0x4f66cb
#10  0x50802b
#11  0x5165af
#12  0x52661f
#13  0x449776
#14  0x449d6f
#15  0x4472e2
#16  0x66d119
#17  0x4026ec
#18  0x7f95ba45bb96
#19  0x40275c
#20  0xffffffffffffffff

Error: 'results.json' not found. Check above for additional error details

1 Ответ

1 голос
/ 14 июля 2020

Мне не удалось воспроизвести вашу проблему, потому что не хватало некоторых входных данных. Вот версия, которая успешно работает как в Windows, так и в Linux. 

from gekko import GEKKO
import time
import numpy as np

now = time.time()
p = GEKKO(remote=False)

#Set variables
sg = p.Var()
rhog = p.Var()
vg = p.Var(value=0)
ag = p.Var(value=0)
thetag = p.Var(value=0)
betag = p.Var(value=0)

curvg = p.Var()
#Parameters
T = 0.5
vref = p.Const(value=3)
nT = 11

#kappa and s reference
arcref = [-1,0,1,2,3,4,5,6]
curvref = [1,2,1,2,1,2,1,2]

p.time = np.linspace(0,nT,nT*2)

p.options.IMODE = 6
p.options.SOLVER = 3
p.options.WEB = 0

p.Obj( rhog**2 + (vg - vref)**2 + ag**2 )

#set kappa estimate
p.cspline(sg, curvg, arcref, curvref)

p.Equation(sg.dt()==vg*p.cos(thetag)/(1-rhog*curvg))
p.Equation(rhog.dt()==vg*p.sin(thetag))
p.Equation(vg.dt()==ag)
p.Equation(thetag.dt()==betag.dt()-curvg*sg.dt())

p.solve(disp=False, debug=True)
print('sg: ' + str(sg.value))
print('curvg: ' + str(curvg.value))
print(f'run time: {time.time()-now}')

Я изменил входные данные cspline на образцы данных и инициализировал sg и rhog на значения по умолчанию (0). Убедитесь, что cspline имеет монотонно возрастающую зависимую переменную.

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