Using GEKKO for Moving Horizon Estimation online 3
This is the following question after Using GEKKO for Moving Horizon Estimation online 2.
My code:
from gekko import GEKKO
import numpy as np
import matplotlib.pyplot as plt
import matplotlib; matplotlib.use('TkAgg')
class Observer():
def __init__(self, window_size, r_init, alpha_init):
self.m = GEKKO(remote=False)
self.dt = 0.05
self.m.time = [i*self.dt for i in range(window_size)]
#Parameters
self.m.u = self.m.MV()
#Variables
self.m.r = self.m.CV(lb=0.01) # value=r_init) #ub=20 can be over 20
self.m.alpha = self.m.CV() # value=alpha_init) #ub lb for angle?
#Equations
self.m.Equation(self.m.r.dt() == -self.m.cos(self.m.alpha))
self.m.Equation(self.m.alpha.dt() == self.m.sin(self.m.alpha)/self.m.r - self.m.u) # differential equation
#Options
# self.m.options.MV_STEP_HOR = 2
self.m.options.IMODE = 5 # dynamic estimation
self.m.options.EV_TYPE = 1 #Default 1: absolute error form 2: squared error form
self.m.options.DIAGLEVEL = 0 #diagnostic level
self.m.options.NODES = 3 #nodes # collocation nodes default:2
self.m.options.SOLVER = 2 #solver_num
# STATUS = 0, optimizer doesn't adjust value
# STATUS = 1, optimizer can adjust
self.m.u.STATUS = 0
self.m.r.STATUS = 1
self.m.alpha.STATUS = 1
# FSTATUS = 0, no measurement
# FSTATUS = 1, measurement used to update model
self.m.u.FSTATUS = 1 #default
self.m.r.FSTATUS = 1
self.m.alpha.FSTATUS = 1
self.m.r.MEAS_GAP = 2
self.m.alpha.MEAS_GAP = 1
self.m.r.TR_INIT = 1
self.m.alpha.TR_INIT = 1
self.count = 0
def MHE(self, observed_state, u_data):
self.count =+ 1
self.m.u.MEAS = u_data
self.m.r.MEAS = observed_state[0]
self.m.alpha.MEAS = observed_state[1]
self.m.solve(disp=True)
return self.m.r.MODEL, self.m.alpha.MODEL
if __name__=="__main__":
FILE_PATH00 = '/home/shane16/Project/model_guard/uav_paper/adversarial/SA_PPO/src/DATA/4end_estimation_results_r.csv'
FILE_PATH01 = '/home/shane16/Project/model_guard/uav_paper/adversarial/SA_PPO/src/DATA/4end_estimation_results_alpha.csv'
FILE_PATH02 = '/home/shane16/Project/model_guard/uav_paper/adversarial/SA_PPO/src/DATA/4end_action_buffer_eps0.0_sig0.0.csv'
cycles = 250
x = np.arange(cycles) # 1...300
matrix00 = np.loadtxt(FILE_PATH00, delimiter=',')
matrix01 = np.loadtxt(FILE_PATH01, delimiter=',')
matrix02 = np.loadtxt(FILE_PATH02, delimiter=',')
vanilla_action_sigma_0 = matrix02
vanilla_estimation_matrix_r = np.zeros(cycles)
vanilla_estimation_matrix_alpha = np.zeros(cycles)
# sigma = 0.0
# vanilla model true/observed states
r_vanilla_sigma_0_true = matrix00[0, 3:] # from step 1
r_vanilla_sigma_0_observed = matrix00[1, 3:] # from step1
alpha_vanilla_sigma_0_true = matrix01[0, 3:]
alpha_vanilla_sigma_0_observed = matrix01[1, 3:]
# initialize estimator
sigma = 0.0 #1.0
solver_num = 2
nodes = 5
# for window_size in [5, 10, 20, 30, 40, 50]:
window_size = 8
observer = Observer(window_size, r_vanilla_sigma_0_observed[0], alpha_vanilla_sigma_0_observed[0])
for i in range(cycles):
if i % 100 == 0:
print('cylcle: {}'.format(i))
vanilla_observed_states = np.hstack((r_vanilla_sigma_0_observed[i], alpha_vanilla_sigma_0_observed[i])) # from current observed state
r_hat, alpha_hat = observer.MHE(vanilla_observed_states, vanilla_action_sigma_0[i]) # and current action -> estimate current state
vanilla_estimation_matrix_r[i] = r_hat
vanilla_estimation_matrix_alpha[i] = alpha_hat
#plot vanilla
plt.figure()
plt.subplot(3,1,1)
plt.title('Vanilla model_sig{}'.format(sigma))
plt.plot(x, vanilla_action_sigma_0[:cycles],'b:',label='action (w)')
plt.legend()
plt.subplot(3,1,2)
plt.ylabel('r')
plt.plot(x, r_vanilla_sigma_0_true[:cycles], 'k-', label='true_r')
plt.plot(x, r_vanilla_sigma_0_observed[:cycles], 'gx', label='observed_r')
plt.plot(x, vanilla_estimation_matrix_r, 'r--', label='time window: 10')
# plt.legend()
plt.subplot(3,1,3)
plt.xlabel('time steps')
plt.ylabel('alpha')
plt.plot(x, alpha_vanilla_sigma_0_true[:cycles], 'k-', label='true_alpha')
plt.plot(x, alpha_vanilla_sigma_0_observed[:cycles], 'gx', label='observed_alpha')
plt.plot(x, vanilla_estimation_matrix_alpha, 'r--', label='time window: {}'.format(window_size))
plt.legend()
plt.savefig('plot/revision/4estimated_STATES_vanilla_sig{}_window{}_cycles{}_solver{}_nodes{}.png'.format(sigma, window_size,cycles, solver_num, nodes))
plt.show()
I have studied and did set the problem as the example https://apmonitor.com/do/index.php/Main/EstimatorTypes.
But when I set window_size in my code over 10, the solution is not found: (result of terminal when options.SOLVER = 0)
apm 165.132.48.158_gk_model0 <br><pre>
---------------------------------------------------------------- APMonitor, Version 1.0.1 APMonitor Optimization Suite
----------------------------------------------------------------
--------- APM Model Size ------------ Each time step contains Objects : 0 Constants : 0 Variables : 3 Intermediates: 0 Connections : 0 Equations : 2 Residuals : 2 Warning: CV( 1 ) on at cycle 1 with no MVs on Warning: CV( 2 ) on at cycle 1 with no MVs on Number of state variables: 261 Number of total equations: - 261 Number of slack variables: - 0 --------------------------------------- Degrees of freedom : 0 ---------------------------------------------- Dynamic Estimation with APOPT Solver
---------------------------------------------- Iter Objective Convergence
0 5.30547E+02 1.04898E+01
1 3.70823E+02 3.25000E-01
2 3.70724E+02 7.49963E-02
3 3.70689E+02 3.74995E-01
4 3.70716E+02 1.00000E-01
5 3.70717E+02 2.00000E-01
6 2.33359E+03 1.73260E-01
7 2.56047E+04 1.00000E-01
8 2.56261E+04 1.18140E-01
9 1.52748E+21 1.39682E+00 Iter Objective Convergence 10 1.08739E+30 1.39682E+00 11 1.06063E+30 1.39682E+00 12
1.03450E+30 1.39682E+00 13 2.40101E+32 1.39682E+00 14 2.34191E+32 1.39682E+00 15 2.28418E+32 1.39682E+00 16 1.68770E+32 1.39682E+00 17 1.64616E+32 1.39682E+00 18 1.60560E+32 1.39682E+00 19 1.72636E+32 1.39682E+00 Iter Objective Convergence 20 1.68387E+32 1.39682E+00 21
1.64239E+32 1.39682E+00 22 1.72644E+32 1.39682E+00 23 1.68395E+32 1.39682E+00 24 1.64243E+32 1.39682E+00 25 1.72645E+32 1.39682E+00 26 1.68395E+32 1.39682E+00 27 1.64243E+32 1.39682E+00 28 1.72645E+32 1.39682E+00 29 1.68395E+32 1.39682E+00 Iter Objective Convergence 30 1.64243E+32 1.39682E+00 31 1.72645E+32 1.39682E+00 32 1.68395E+32 1.39682E+00 33 1.64244E+32 1.39682E+00 34 1.72645E+32 1.39682E+00 35 1.68395E+32 1.39682E+00 36 1.64244E+32 1.39682E+00 37 1.72645E+32 1.39682E+00 38 1.68395E+32 1.39682E+00 39 1.64244E+32 1.39682E+00 Iter Objective Convergence 40 1.72645E+32 1.39682E+00 41
1.68395E+32 1.39682E+00 42 1.64244E+32 1.39682E+00 43 1.72645E+32 1.39682E+00 44 1.68395E+32 1.39682E+00 45 1.64245E+32 1.39682E+00 46 1.72645E+32 1.39682E+00 47 1.68395E+32 1.39682E+00 48 1.64243E+32 1.39682E+00 49 1.72645E+32 1.39682E+00 Iter Objective Convergence 50 1.68395E+32 1.39682E+00 51 1.64243E+32 1.39682E+00 52 1.72645E+32 1.39682E+00 53 1.68395E+32 1.39682E+00 54 1.64244E+32 1.39682E+00 55 1.72645E+32 1.39682E+00 56 1.68395E+32 1.39682E+00 57 1.64244E+32 1.39682E+00 58 1.72645E+32 1.39682E+00 59 1.68395E+32 1.39682E+00 Iter Objective Convergence 60 1.64244E+32 1.39682E+00 61
1.72645E+32 1.39682E+00 62 1.68395E+32 1.39682E+00 63 1.64243E+32 1.39682E+00 64 1.72645E+32 1.39682E+00 65 1.68395E+32 1.39682E+00 66 1.64243E+32 1.39682E+00 67 1.72645E+32 1.39682E+00 68 1.68395E+32 1.39682E+00 69 1.64244E+32 1.39682E+00 Iter Objective Convergence 70 1.72645E+32 1.39682E+00 71 1.68395E+32 1.39682E+00
... 81 1.64244E+32 1.39682E+00 82 1.72645E+32 1.39682E+00 83 1.68395E+32 1.39682E+00 84 1.64243E+32 1.39682E+00 85 1.72645E+32 1.39682E+00 86 1.68395E+32 1.39682E+00 87 1.64243E+32 1.39682E+00 88 1.72645E+32 1.39682E+00 89 1.68395E+32 1.39682E+00 Iter Objective Convergence 90 1.64243E+32 1.39682E+00 91 1.72645E+32 1.39682E+00 92 1.68395E+32 1.39682E+00 93 1.64243E+32 1.39682E+00 94 1.72645E+32 1.39682E+00 95 1.68395E+32 1.39682E+00 96 1.64243E+32 1.39682E+00 97 1.72645E+32 1.39682E+00 98 1.68395E+32 1.39682E+00 99 1.64243E+32 1.39682E+00 Iter Objective Convergence 100 1.72645E+32 1.39682E+00 101 1.68395E+32 1.39682E+00 102 1.64244E+32 1.39682E+00 103 1.72645E+32 1.39682E+00 104 1.68395E+32 1.39682E+00 105 1.64244E+32 1.39682E+00 106 1.72645E+32 1.39682E+00 107 1.68395E+32 1.39682E+00 108 1.64244E+32 1.39682E+00 109 1.72645E+32 1.39682E+00 Iter Objective Convergence 110 1.68395E+32 1.39682E+00 111 1.64243E+32 1.39682E+00 112 1.72645E+32 1.39682E+00 113 1.68395E+32 1.39682E+00 114 1.64243E+32 1.39682E+00 115 1.72645E+32 1.39682E+00 116 1.68395E+32 1.39682E+00 117 1.64244E+32 1.39682E+00 118 1.72645E+32 1.39682E+00 119 1.68395E+32 1.39682E+00 Iter Objective Convergence 120 1.64244E+32 1.39682E+00 121 1.72645E+32 1.39682E+00 122 1.68395E+32 1.39682E+00 123 1.64243E+32 1.39682E+00 124 1.72645E+32 1.39682E+00 125 1.68395E+32 1.39682E+00 126 1.64244E+32 1.39682E+00 127 1.72645E+32 1.39682E+00 128 1.68395E+32 1.39682E+00 129 1.64243E+32 1.39682E+00 Iter Objective Convergence 130 1.72645E+32 1.39682E+00 131 1.68395E+32 1.39682E+00 132 1.64244E+32 1.39682E+00 133 1.72645E+32 1.39682E+00 134 1.68395E+32 1.39682E+00 135 1.64243E+32 1.39682E+00 136 1.72645E+32 1.39682E+00 137 1.68395E+32 1.39682E+00 138 1.64243E+32 1.39682E+00 139 1.72645E+32 1.39682E+00 Iter Objective Convergence 140 1.68395E+32 1.39682E+00 141 1.64243E+32 1.39682E+00 142 1.72645E+32 1.39682E+00 143 1.68395E+32 1.39682E+00 144 1.64243E+32 1.39682E+00 145 1.72645E+32 1.39682E+00 146 1.68395E+32 1.39682E+00 147 1.64244E+32 1.39682E+00 148 1.72645E+32 1.39682E+00 149 1.68395E+32 1.39682E+00 Iter Objective Convergence 150 1.64243E+32 1.39682E+00 151 1.72645E+32 1.39682E+00 152 1.68395E+32 1.39682E+00 153 1.64244E+32 1.39682E+00 154 1.72645E+32 1.39682E+00 155 1.68395E+32 1.39682E+00 156 1.64244E+32 1.39682E+00 157 1.72645E+32 1.39682E+00 158 1.68395E+32 1.39682E+00 159 1.64243E+32 1.39682E+00 Iter Objective Convergence 160 1.72645E+32 1.39682E+00 161 1.68395E+32 1.39682E+00 162 1.64243E+32 1.39682E+00 163 1.72645E+32 1.39682E+00 164 1.68395E+32 1.39682E+00 165 1.64244E+32 1.39682E+00 166 1.72645E+32 1.39682E+00 167 1.68395E+32 1.39682E+00 168 1.64244E+32 1.39682E+00 169 1.72645E+32 1.39682E+00 Iter Objective Convergence 170 1.68395E+32 1.39682E+00 171 1.64243E+32 1.39682E+00 172 1.72645E+32 1.39682E+00 173 1.68395E+32 1.39682E+00 174 1.64244E+32 1.39682E+00 175 1.72645E+32 1.39682E+00 176 1.68395E+32 1.39682E+00 177 1.64243E+32 1.39682E+00 178 1.72645E+32 1.39682E+00 179 1.68395E+32 1.39682E+00 Iter Objective Convergence 180 1.64244E+32 1.39682E+00 181 1.72645E+32 1.39682E+00 182 1.68395E+32 1.39682E+00 183 1.64243E+32 1.39682E+00 184 1.72645E+32 1.39682E+00 185 1.68395E+32 1.39682E+00 186 1.64243E+32 1.39682E+00 187 1.72645E+32 1.39682E+00 188 1.68395E+32 1.39682E+00 189 1.64243E+32 1.39682E+00 Iter Objective Convergence 190 1.72645E+32 1.39682E+00 191 1.68395E+32 1.39682E+00 192 1.64243E+32 1.39682E+00 193 1.72645E+32 1.39682E+00 194 1.68395E+32 1.39682E+00 195 1.64244E+32 1.39682E+00 196 1.72645E+32 1.39682E+00 197 1.68395E+32 1.39682E+00 198 1.64243E+32 1.39682E+00 199 1.72645E+32 1.39682E+00 Iter Objective Convergence 200 1.68395E+32 1.39682E+00 201 1.64244E+32 1.39682E+00 202 1.72645E+32 1.39682E+00 203 1.68395E+32 1.39682E+00 204 1.64244E+32 1.39682E+00 205 1.72645E+32 1.39682E+00 206 1.68395E+32 1.39682E+00 207 1.64243E+32 1.39682E+00 208 1.72645E+32 1.39682E+00 209 1.68395E+32 1.39682E+00 Iter Objective Convergence 210 1.64243E+32 1.39682E+00 211 1.72645E+32 1.39682E+00 212 1.68395E+32 1.39682E+00 213 1.64244E+32 1.39682E+00 214 1.72645E+32 1.39682E+00 215 1.68395E+32 1.39682E+00 216 1.64244E+32 1.39682E+00 217 1.72645E+32 1.39682E+00 218 1.68395E+32 1.39682E+00 219 1.64243E+32 1.39682E+00 Iter Objective Convergence 220 1.72645E+32 1.39682E+00 221 1.68395E+32 1.39682E+00 222 1.64244E+32 1.39682E+00 223 1.72645E+32 1.39682E+00 224 1.68395E+32 1.39682E+00 225 1.64243E+32 1.39682E+00 226 1.72645E+32 1.39682E+00 227 1.68395E+32 1.39682E+00 228 1.64244E+32 1.39682E+00 229 1.72645E+32 1.39682E+00 Iter Objective Convergence 230 1.68395E+32 1.39682E+00 231 1.64243E+32 1.39682E+00 232 1.72645E+32 1.39682E+00 233 1.68395E+32 1.39682E+00 234 1.64243E+32 1.39682E+00 235 1.72645E+32 1.39682E+00 236 1.68395E+32 1.39682E+00 237 1.64243E+32 1.39682E+00 238 1.72645E+32 1.39682E+00 239 1.68395E+32 1.39682E+00 Iter Objective Convergence 240 1.64243E+32 1.39682E+00 241 1.72645E+32 1.39682E+00 242 1.68395E+32 1.39682E+00 243 1.64244E+32 1.39682E+00 244 1.72645E+32 1.39682E+00 245 1.68395E+32 1.39682E+00 246 1.64243E+32 1.39682E+00 247 1.72645E+32 1.39682E+00 248 1.68395E+32 1.39682E+00 249 1.64244E+32 1.39682E+00 Iter Objective Convergence 250 1.72645E+32 1.39682E+00 Maximum iterations --------------------------------------------------- Solver : APOPT (v1.0) Solution time : 5.02409999999873 sec Objective : 217.772371342953 Unsuccessful with error code 0 --------------------------------------------------- ---------------------------------------------- Dynamic Estimation with BPOPT Solver ----------------------------------------------
----------------------------------------------------- BPOPT Solver v1.0.6
----------------------------------------------------- Adjusting variables to interior region of bounds Iter Objective Convergence
0 -1.85748E+02 3.38018E+01
1 -1.05777E+02 2.71532E+01
2 1.26905E+02 2.76867E+02
3 4.04640E+03 7.58592E+02
4 1.22410E+08 1.22407E+04
5 1.88476E+03 1.95147E+04
-1.77050E+00 4.25888E+02
9.23784E+02 9.96666E+03
1.38670E+03 1.47370E+04
1.61835E+03 1.71234E+04
1.74542E+03 1.83168E+04
6 1.81543E+03 1.89153E+04
2.56695E+02 1.43715E+03
1.01483E+03 1.00785E+04
1.40039E+03 1.44630E+04
1.59401E+03 1.66629E+04
1.69819E+03 1.77867E+04
7 1.75705E+03 1.83500E+04
8 6.72094E+08 6.72094E+04
5.65658E+02 6.07154E+03
3.69827E+03 3.62246E+04
5.28094E+03 5.14597E+04
6.09958E+03 5.93489E+04
6.50835E+03 6.32875E+04
9 6.71243E+03 6.52535E+04 10 3.42908E+02 3.74813E+03 11 8.25957E+03 3.79110E+03 12 4.75089E+07 4.75089E+03 13 1.75564E+04 1.44171E+04
7.14522E+07 7.14522E+03
9.29139E+07 9.29140E+03
1.14506E+08 1.14506E+04
1.26204E+08 1.26204E+04
1.32081E+08 1.32081E+04 14 1.37395E+08 1.37395E+04 Iter Objective Convergence 15 9.73361E+07 9.73356E+03 16
5.10815E+08 5.10812E+04
3.34519E+03 1.54614E+04
5.68490E+03 3.27431E+04
6.90872E+03 4.19233E+04
7.53574E+03 4.66639E+04
7.82826E+03 4.88168E+04 17 7.97497E+03 4.98979E+04 18 1.02392E+09 1.02392E+05 19 7.77468E+09 7.77468E+05 20 9.02530E+09 1.30137E+06 21 8.22402E+12 8.22402E+08
8.27849E+07 7.85323E+08
6.67868E+07 6.46502E+08
6.68851E+07 6.58066E+08
7.40486E+07 7.34991E+08
7.80379E+07 7.77529E+08 22 8.00766E+07 7.99239E+08 23 8.85462E+12 8.85424E+08
3.10775E+08 2.89271E+08
3.88079E+08 5.70603E+08
4.28405E+08 7.28006E+08
4.48567E+08 8.06703E+08
4.58649E+08 8.46059E+08 24 4.63690E+08 8.65737E+08 25 1.86029E+07 1.48320E+08
1.17713E+10 1.17712E+06
7.44218E+11 7.44216E+07
1.11371E+12 1.11370E+08
1.29845E+12 1.29844E+08
1.39082E+12 1.39082E+08 26 1.43700E+12 1.43700E+08
9.97937E+09 9.97933E+05
7.20196E+11 7.20194E+07
1.07860E+12 1.07860E+08
1.25780E+12 1.25780E+08
1.34740E+12 1.34740E+08 27 1.39221E+12 1.39220E+08
4.87457E+09 4.87453E+05
6.97347E+11 6.97346E+07
1.04477E+12 1.04477E+08
1.21849E+12 1.21848E+08
1.30535E+12 1.30534E+08 28 1.34878E+12 1.34877E+08
7.02507E+04 6.33467E+05
8.46417E+06 6.74433E+07
1.26923E+07 1.01160E+08
1.48064E+07 1.18019E+08
1.58634E+07 1.26448E+08 29 1.63920E+07 1.30662E+08 Iter Objective Convergence 30 6.88703E+05 1.60107E+06
1.15163E+08 8.31826E+05
1.68185E+08 1.21658E+06
1.94691E+08 1.40891E+06
2.07914E+08 1.50487E+06
2.14555E+08 1.55306E+06 31 2.17836E+08 1.57686E+06 *** WARNING MESSAGE FROM SUBROUTINE MA27BD *** INFO(1) = 3
MATRIX IS SINGULAR. RANK= 683 Problem with linear solver, INFO: 3 --------------------------------------------------- Solver : BPOPT (v1.0) Solution time : 4.249999999956344E-002 sec Objective : 528860.935305211 Unsuccessful with error code 0 ---------------------------------------------------
********************************************** Dynamic Estimation with Interior Point Solver
**********************************************
Info: Exact Hessian
****************************************************************************** This program contains Ipopt, a library for large-scale nonlinear optimization. Ipopt is released as open source code under the Eclipse Public License (EPL).
For more information visit http://projects.coin-or.org/Ipopt
******************************************************************************
This is Ipopt version 3.12.10, running with linear solver ma57.
Number of nonzeros in equality constraint Jacobian...: 257 Number of nonzeros in inequality constraint Jacobian.: 324 Number of nonzeros in Lagrangian Hessian.............: 54
Total number of variables............................: 261
variables with only lower bounds: 180
variables with lower and upper bounds: 0
variables with only upper bounds: 0 Total number of equality constraints.................: 99 Total number of inequality constraints...............: 162
inequality constraints with only lower bounds: 162 inequality constraints with lower and upper bounds: 0
inequality constraints with only upper bounds: 0
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls 0 8.8000164e-01 1.05e+01 9.00e+00 0.0 0.00e+00 -
0.00e+00 0.00e+00 0 1 1.0609900e+00 1.05e+01 9.02e+00 -6.7 3.88e+01 - 1.84e-03 1.78e-03h 1 2 9.3143493e+00 1.02e+01 2.21e+01 0.4 3.87e+01 - 1.79e-02 1.98e-02f 1 3 9.3142593e+00 1.02e+01 1.15e+04 -0.3 3.79e+01 - 2.86e-01 2.02e-04h 1 4r 9.3142593e+00 1.02e+01 1.00e+03 1.0 0.00e+00 - 0.00e+00 2.53e-07R 4 5r 5.3654124e+01 8.37e+00 1.16e+03 1.6 2.57e+02 - 2.05e-03 7.22e-03f 1 6 5.3675353e+01 8.36e+00 2.99e+02 -6.2 4.01e+01 - 2.12e-01 7.00e-04h 1 7r 5.3675353e+01 8.36e+00 9.99e+02 0.9 0.00e+00 - 0.00e+00 4.38e-07R 5 8r 1.6618000e+02 2.86e+00 9.90e+02 1.0 6.80e+02 - 2.20e-02 8.16e-03f 1 9 1.6613771e+02 2.86e+00 7.01e+02 -6.2 3.78e+01 - 4.05e-01 5.72e-04h 1 iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls 10r 1.6613771e+02
2.86e+00 9.99e+02 0.5 0.00e+00 - 0.00e+00 3.58e-07R 5 11r 2.2518286e+02 1.89e+00 9.97e+02 1.8 1.58e+03 - 5.31e-03 1.80e-03f 1 12 2.2512388e+02 1.89e+00 1.12e+03 -6.1 3.77e+01 - 4.42e-01 3.90e-04f 1 13r 2.2512388e+02 1.89e+00 1.00e+03 0.3 0.00e+00 - 0.00e+00 4.87e-07R 4 14r 2.2721384e+02 1.87e+00 9.91e+02 -5.9 6.07e+01 - 3.73e-03 7.55e-03f 1 15r 2.2764670e+02 6.34e-01 9.89e+02 1.5 2.10e+04 - 3.96e-03 1.18e-03f 1 16 2.2763736e+02 6.34e-01 5.40e+03 -6.1 1.48e+02 - 4.36e-01 7.99e-05h 1 17r 2.2763736e+02 6.34e-01 1.00e+03 -0.0 0.00e+00 - 0.00e+00 4.00e-07R 2 18r 2.3088007e+02 5.58e-01 9.95e+02 1.9 9.63e+02 - 7.10e-03 2.87e-03f 1 19 2.3089464e+02 5.58e-01 5.63e+04 0.1 1.19e+02 - 4.79e-01 4.76e-04h 1 iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls 20r 2.3089464e+02 5.58e-01 1.00e+03
-0.3 0.00e+00 - 0.00e+00 2.98e-07R 5 21r 2.3319530e+02 5.24e-01 1.31e+03 1.7 1.33e+03 - 1.50e-02 3.54e-03f 1 22r 2.5899287e+02 3.78e-01 1.77e+03 1.9 1.04e+02 - 5.59e-02 4.32e-02f 1 23 2.5842489e+02 3.78e-01 6.85e+02 0.2 6.86e+01 - 8.90e-01 1.48e-03f 3 24 2.5843511e+02 3.82e-01 3.36e+04 0.2 6.84e+01 - 2.20e-01 4.46e-03f 1 25 2.5843515e+02 3.82e-01 1.36e+08 0.2 6.48e+01 - 1.80e-01 4.47e-05h 1 26r 2.5843515e+02 3.82e-01 1.00e+03 0.2 0.00e+00 - 0.00e+00 2.24e-07R 2 27r 2.6284498e+02 2.08e-01 1.34e+03 1.9 1.55e+02 - 7.63e-02 5.34e-03f 1 28 2.6244784e+02 2.08e-01 4.34e+03 0.2 4.59e+01 - 9.14e-01 9.61e-04h 1 29r 2.6244784e+02 2.08e-01 1.00e+03 0.2 0.00e+00 - 0.00e+00 3.01e-07R 6 iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls 30r
2.7090035e+02 2.28e-01 9.50e+02 1.6 7.37e+01 - 2.96e-01 1.63e-02f 1 31r 2.7157286e+02 2.27e-01 9.22e+02 0.4 2.45e+00 - 4.94e-01 3.05e-02f 1 32r 2.7252200e+02 2.29e-01 5.15e+02 -1.1 1.18e+00 - 8.32e-01 4.55e-01f 1 33r 2.8772420e+02 2.25e-01 9.40e+01 -0.7 2.22e+00 - 9.83e-01 9.15e-01f 1 34r 2.8769913e+02 1.95e+00 1.26e+02 -6.6 1.40e+03 - 1.66e-04 1.08e-03f 1 35r 2.9223102e+02 1.54e+00 1.29e+03 -1.2 1.05e+00 0.0 3.03e-01 8.71e-01f 1 36r 2.9225465e+02 1.07e+00 9.01e+02 -0.9 5.35e-01 2.2 4.81e-01 6.15e-01f 1 37r 2.9231013e+02 5.11e-01 1.06e+03 -0.4 2.19e-01 2.7 1.36e-01 1.00e+00f 1 38r 2.9231181e+02 4.23e-01 9.15e+02 -0.6 1.86e-01 3.1 9.06e-02 1.77e-01f 1 39r 2.9231198e+02 4.04e-01 1.12e+03 -0.6 2.11e-01 3.5 2.88e-01 4.46e-02f 1 iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls 40r 2.9231360e+02 3.01e-01
9.53e+02 -0.6 2.60e-01 3.0 6.51e-02 1.35e-01f 1 41r 2.9231693e+02 2.72e-01 1.66e+03 -0.6 2.67e-01 2.6 1.00e+00 9.33e-02f 1 42r 2.9232719e+02 1.98e-01 2.41e+02 -0.6 1.29e-01 3.0 2.20e-01 7.65e-01h 1 43r 2.9243143e+02 2.09e-01 5.65e+02 0.3 2.98e-01 2.5 1.00e+00 2.52e-01f 1 44r 2.9246350e+02 2.10e-01 8.61e+02 -0.4 2.92e-01 2.0 9.92e-01 2.01e-01f 1 45r 2.9245480e+02 2.09e-01 1.93e+02 -1.4 1.20e-01 2.5 1.00e+00 7.37e-01f 1 46r 2.9259452e+02 2.03e-01 1.27e+03 0.2 1.80e+00 2.0 7.20e-01 1.20e-01f 1 47r 2.9277900e+02 2.04e-01 7.72e+02 -0.3 1.25e+00 1.5 3.93e-01 2.34e-01f 1 48r 2.9280994e+02 2.04e-01 5.33e+02 -0.3 1.78e+00 1.0 3.76e-01 1.16e-02h 1 49r 2.9962583e+02 2.28e-01 3.45e+02 -0.3 7.89e-01 0.5 7.13e-01 1.00e+00f 1 iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls 50r 3.2677031e+02 4.59e-01 7.44e+01
-0.3 6.06e-01 - 1.00e+00 7.82e-01f 1 51r 4.2678794e+02 4.44e-01 1.12e+01 -0.3 4.39e+00 - 1.00e+00 1.00e+00f 1 52r 3.4495773e+02 1.99e-01 1.01e+01 -1.0 2.60e+00 - 8.72e-01 1.00e+00f 1 53r 3.4520580e+02 2.23e-01 3.63e+02 -1.0 4.22e-01 0.1 1.00e+00 3.00e-01f 2 54r 3.2340242e+02 2.25e-01 2.00e+00 -1.1 1.11e+00 - 1.00e+00 1.00e+00f 1 55r 2.9817629e+02 2.31e-01 6.43e+01 -2.2 7.79e-01 - 9.99e-01 7.57e-01f 1 56r 2.8673872e+02 2.25e-01 4.58e-01 -2.7 2.41e-01 - 1.00e+00 1.00e+00f 1 57r 2.7428826e+02 2.23e-01 8.35e-02 -3.9 3.26e-01 - 1.00e+00 1.00e+00f 1 58r 2.7154701e+02 2.21e-01 1.36e+00 -4.8 2.86e+00 - 9.99e-01 6.82e-01f 1 59r 2.7155377e+02 2.21e-01 5.33e-03 -4.2 2.28e-02 -0.4 1.00e+00 1.00e+00h 1 iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls 60r
2.7041602e+02 2.21e-01 8.88e+00 -4.9 4.62e+00 - 9.97e-01 1.64e-01h 1 61r 2.7039401e+02 2.21e-01 1.33e-02 -6.0 7.91e-02 -0.9 1.00e+00 9.97e-01h 1 62r 2.7037446e+02 2.21e-01 1.52e-02 -7.6 3.26e-01 -1.4 1.00e+00 1.00e+00f 1 63r 2.7036542e+02 2.21e-01 1.24e-01 -8.6 1.25e+00 -1.8 1.00e+00 1.00e+00f 1 64r 2.7035672e+02 2.21e-01 3.74e+00 -9.0 7.13e+00 -2.3 1.00e+00 1.00e+00f 1 65r 2.7035462e+02 2.21e-01 7.83e-01 -8.7 3.27e+00 -1.9 1.00e+00 1.00e+00h 1 66r 2.7034622e+02 5.19e-01 3.07e+01 -8.5 2.10e+01 -2.4 1.00e+00 1.00e+00f 1 67r 2.7034197e+02 2.66e-01 7.12e+00 -8.8 1.02e+01 -1.9 1.00e+00 1.00e+00f 1 68r 2.7033259e+02 3.97e+01 2.03e+02 -8.9 9.24e+01 -2.4 1.00e+00 1.00e+00f 1 69r 2.6360194e+02 1.39e+01 5.98e+02 -7.3 4.14e+01 - 1.00e+00 1.00e+00h 1 iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls 70r 2.6287479e+02 1.17e+01
4.25e+02 -7.1 1.33e+01 - 1.00e+00 1.00e+00h 1 71r 2.6399459e+02 4.20e+00 3.71e+02 -6.2 1.24e+01 - 1.00e+00 6.63e-01h 1 72r 2.6277485e+02 2.15e-01 1.34e+00 -6.7 5.00e+00 - 1.00e+00 1.00e+00h 1 73r 2.6249804e+02 2.14e-01 8.71e-02 -8.0 2.35e-01 - 1.00e+00 1.00e+00h 1 74r 2.6246138e+02 2.14e-01 1.06e-01 -9.0 1.43e-01 - 1.00e+00 1.00e+00h 1 75r 2.6248456e+02 2.15e-01 3.45e-03 -9.0 2.17e-02 - 1.00e+00 1.00e+00h 1 76r 2.6248458e+02 2.15e-01 3.74e-03 -9.0 2.15e-03 - 1.00e+00 1.00e+00h 1 77r 2.6248458e+02 2.15e-01 1.26e-04 -9.0 4.26e-04 - 1.00e+00 1.00e+00h 1
Number of Iterations....: 77
(scaled) (unscaled) Objective...............: 2.6248457642008947e+02
2.6248457642008947e+02 Dual infeasibility......: 1.9999999998163066e+01 1.9999999998163066e+01 Constraint violation....: 2.1450238157252022e-01 2.1450238157252022e-01 Complementarity.........: 1.0000004294468675e-09
1.0000004294468675e-09 Overall NLP error.......: 1.9999999998163066e+01 1.9999999998163066e+01
Number of objective function evaluations = 118 Number of objective gradient evaluations = 29 Number of equality constraint evaluations = 118 Number of inequality constraint evaluations = 118 Number of equality constraint Jacobian evaluations = 87 Number of inequality constraint Jacobian evaluations = 87 Number of Lagrangian Hessian evaluations
= 78 Total CPU secs in IPOPT (w/o function evaluations) = 0.131 Total CPU secs in NLP function evaluations = 0.053
EXIT: Converged to a point of local infeasibility. Problem may be infeasible. An error occured. The error code is 2
and if I set window_size = 5, the estimation result does not follow true states:
What am I doing wrong? How should I fix this?
Sorry if I'm asking something that is easily known through studying example, but I still don't get the solution. Thank you for your kind instruction.
Sincerely, Shane K.
The objective function value from the solver iterations gives a clue that one of the variables is getting very large. It could be related to the divide-by-zero issue that is in the response to Using GEKKO for Moving Horizon Estimation online 2.
One of the equations may be the source of the problem:
self.m.alpha.dt() == self.m.sin(self.m.alpha)/self.m.r - self.m.u
The initial value of r is zero (default) because no initial value is provided when it is declared as self.m.r = self.m.CV(lb=0). A comment suggests that it was formerly initialized with value r_init. The zero value creates a divide-by-zero for that equation. Try rearranging the equation into an equivalent form that avoids the potential for divide-by-zero either with the initial guess or when the solver is iterating.
self.m.r*self.m.alpha.dt() == self.m.sin(self.m.alpha) - self.m.r*self.m.u
The initialization strategies article also gives suggestions on methods to obtain a successful solution:
Safdarnejad, S.M., Hedengren, J.D., Lewis, N.R., Haseltine, E., Initialization Strategies for Optimization of Dynamic Systems, Computers and Chemical Engineering, 2015, Vol. 78, pp. 39-50, DOI: 10.1016/j.compchemeng.2015.04.016.
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