How can you fix initial conditions in Gekko?? I am pretty new to Gekko still and am working on optimizing the AOA and bank angles for a shuttle-type reentry vehicle to maximize cross-range. The EOMs are 6 coupled, non-linear ODEs. Right now I can only get a solution on small time horizons (about 2 seconds) and by providing bounds on the initial condition instead of making it fixed. The figure below shows a solution where the altitude begins at around 0 meters when I need it to start at 79,248 meters. I can't get convergence without providing bounds on the state variables.
from gekko import GEKKO
import numpy as np
import matplotlib.pyplot as plt
import math
pi = math.pi
########################
######FRONT MATTER######
########################
m = GEKKO() # initialize GEKKO
tfin = 1
nt = 101 #simulation time is 2500 seconds
m.time = np.linspace(0,tfin,nt) #time array
#==================#
#PARAMS
#==================#
Re = m.Param(value = 6371203.92) # radius of the earth, m
S = m.Param(value = 249.9091776) # vehicle surface area, m^2
cl0 = m.Param(value = -0.2070) # coeff lift param 1
cl1 = m.Param(value = 1.6756) # coeff lift param 2
cd0 = m.Param(value = 0.0785) # coeff drag param 1
cd1 = m.Param(value = -0.3529) # coeff drag param 2
cd2 = m.Param(value = 2.0400) # coeff drag param 3
H = m.Param(value = 7254.24) # density scale height, m
rho0= m.Param(value = 1.225570827014494) # sea level atmospheric density, kg/m^3
mu = m.Param(value = 3.986031954093051e14) #earth gravitational param, m^3/s^2
mass= m.Param(value = 92079.2525560557) #vehicle mass, kg
#===============================#
#BOUNDARY CONDITIONS
#===============================#
t0 = 0
alt0 = 79248
rad0 = alt0+Re
altf = 24384
radf = altf+Re
lon0 = 0
lat0 = 0
speed0 = +7802.88
speedf = +762
fpa0 = -1*pi/180
fpaf = -5*pi/180
azi0 = +90*pi/180
azif = -90*pi/180
#===============================#
#LIMITS ON VARIABLES
#===============================#
tfMin = 0; tfMax = 3000;
radMin = Re; radMax = rad0;
lonMin = -pi; lonMax = -lonMin;
latMin = -70*pi/180; latMax = -latMin;
speedMin = 10; speedMax = 45000;
fpaMin = -80*pi/180; fpaMax = 80*pi/180;
aziMin = -180*pi/180; aziMax = 180*pi/180;
aoaMin = -90*pi/180; aoaMax = -aoaMin;
bankMin = -90*pi/180; bankMax = 1*pi/180;
#===============================#
#VARIABLES
#===============================#
#state variables and bounds
rad = m.Var(value=rad0, lb=radMin, ub=radMax) # radius, m
lon = m.Var(value=lon0, lb=lonMin, ub=lonMax) # longitude, rad
lat = m.Var(value=lat0, lb=latMin, ub=latMax) # latitude, rad
vel = m.Var(value=speed0, lb=speedMin, ub=speedMax) # velocity, m/sec
fpa = m.Var(value=fpa0, lb=fpaMin, ub=fpaMax) # flight path angle, rad
azi = m.Var(value=azi0, lb=aziMin, ub=aziMax) # azimuth angle, rad
#control variables
aoa = m.MV(value=20*pi/180, lb=aoaMin, ub=aoaMax) # angle of attack, rad
aoa.STATUS = 1
# aoa = m.Const(value=17) # angle of attack, rad
bank = m.MV(value=0, lb=bankMin, ub=bankMax) # bank angle, rad
bank.STATUS = 1
# bank.DCOST = 1e-2
# bank = m.Const(value=0) # bank angle, rad
#===============================#
#INTERMEDIATE VARIABLES
#===============================#
altitude = m.Intermediate(rad - Re)
CD = m.Intermediate(cd0+cd1*aoa+cd2*aoa**2)
rho = m.Intermediate(rho0*m.exp(-altitude/H))
CL = m.Intermediate(cl0+cl1*aoa)
q = m.Intermediate(0.5*rho*vel**2)
D = m.Intermediate(q*S*CD/mass)
L = m.Intermediate(q*S*CL/mass)
gravity = m.Intermediate(mu/rad**2)
#===============================#
#EOMS
#===============================#
p = np.zeros(nt) # mark final time point
p[-1] = 1.0
final = m.Param(value=p)
m.Equation(rad.dt() == vel*m.sin(fpa))
m.Equation(lon.dt()*(rad*m.cos(lat)) == vel*m.cos(fpa)*m.sin(azi))
m.Equation(lat.dt()*rad == vel*m.cos(fpa)*m.cos(azi))
m.Equation(vel.dt() == -D-gravity*m.sin(fpa))
m.Equation(fpa.dt()*vel == (L*m.cos(bank)-m.cos(fpa)*(gravity-vel**2/rad)))
m.Equation(azi.dt()*vel == (L*m.sin(bank)/m.cos(fpa)+vel**2*m.cos(fpa)*m.sin(azi)*m.tan(lat)/rad))
#===============================#
#OPTIMIZATION SOLVER
#===============================#
m.Maximize(lat*final)
# m.options.SOLVER = 3
# m.options.IMODE = 6
# m.solve(disp=True)
# m.options.MAX_ITER = 500
m.options.IMODE = 6
# m.options.NODES = 3
# m.options.MV_TYPE = 1
m.options.SOLVER = 3
# m.open_folder()
m.solve()
#===============================#
#PLOTS
#===============================#
alt = np.array(rad.value)
alt = alt-Re
vel = np.array(vel.value)/1000
latitude = np.array(lat.value)*180/pi
longitude = np.array(lon.value)*180/pi
fpa = np.array(fpa.value)*180/pi
azi = np.array(azi.value)*180/pi
aoa = np.array(aoa.value)*180/pi
bank = np.array(bank.value)*180/pi
plt.subplot(4,2,1)
plt.plot(m.time,alt,label='alt')
plt.legend()
plt.subplot(4,2,3)
plt.plot(m.time,latitude,label='lat')
plt.legend()
plt.subplot(4,2,4)
plt.plot(m.time,longitude,label='lon')
plt.legend()
plt.subplot(4,2,2)
plt.plot(m.time,vel,label='vel')
plt.legend()
plt.subplot(4,2,5)
plt.plot(m.time,fpa,label='fpa')
plt.legend()
plt.subplot(4,2,6)
plt.plot(m.time,azi,label='azi')
plt.legend()
plt.subplot(4,2,7)
plt.plot(m.time,aoa,label='aoa')
plt.xlabel('Time')
plt.legend()
plt.subplot(4,2,8)
plt.plot(m.time,bank,label='bank')
plt.xlabel('Time')
plt.legend()
plt.show()
