Hyper-Sensitive Problem¶
This example is based on the Hyper-Sensitive problem given in Patterson1. In this problem we seek to minimize both the distance traveled when moving between fixed boundary conditions and also to minimize the control u used. The cost function to be minimized is:
The system is subject to the dynamic constraints:
The boundary conditions are:
The control u is unconstrained while the final time t_f is fixed.
Due to the nature of dynamics, for sufficiently large values of t_f, the problem exhibits a dive, cruise, and resurface type structure, where the all interesting behavior occurs at the beginning and end while remaining relatively constant in the middle.
This problem has a known analytic optimal solution:
where:
The ODE System: hyper_sensitive_ode.py¶
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Building and running the problem¶
The following code shows the procedure for solving the problem
import openmdao.api as om
from openmdao.utils.assert_utils import assert_near_equal
import dymos as dm
from dymos.examples.plotting import plot_results
from dymos.examples.hyper_sensitive.hyper_sensitive_ode import HyperSensitiveODE
# Initialize the problem and assign the driver
p = om.Problem(model=om.Group())
p.driver = om.pyOptSparseDriver()
p.driver.options['optimizer'] = 'SLSQP'
p.driver.declare_coloring()
# Setup the trajectory and its phase
traj = p.model.add_subsystem('traj', dm.Trajectory())
transcription = dm.Radau(num_segments=30, order=3, compressed=False)
phase = traj.add_phase('phase0',
dm.Phase(ode_class=HyperSensitiveODE, transcription=transcription))
phase.set_time_options(fix_initial=True, fix_duration=True)
phase.add_state('x', fix_initial=True, fix_final=False, rate_source='x_dot', targets=['x'])
phase.add_state('xL', fix_initial=True, fix_final=False, rate_source='L', targets=['xL'])
phase.add_control('u', opt=True, targets=['u'])
phase.add_boundary_constraint('x', loc='final', equals=1)
phase.add_objective('xL', loc='final')
p.setup(check=True)
p.set_val('traj.phase0.states:x', phase.interpolate(ys=[1.5, 1], nodes='state_input'))
p.set_val('traj.phase0.states:xL', phase.interpolate(ys=[0, 1], nodes='state_input'))
p.set_val('traj.phase0.t_initial', 0)
p.set_val('traj.phase0.t_duration', tf)
p.set_val('traj.phase0.controls:u', phase.interpolate(ys=[-0.6, 2.4], nodes='control_input'))
#
# Solve the problem.
#
dm.run_problem(p)
#
# Verify that the results are correct.
#
ui, uf, J = solution()
#
# Simulate the explicit solution and plot the results.
#
exp_out = traj.simulate()
plot_results([('traj.phase0.timeseries.time', 'traj.phase0.timeseries.states:x',
'time (s)', 'x $(m)$'),
('traj.phase0.timeseries.time', 'traj.phase0.timeseries.controls:u',
'time (s)', 'u $(m/s^2)$')],
title='Hyper Sensitive Problem Solution\nRadau Pseudospectral Method',
p_sol=p, p_sim=exp_out)
plt.show()
INFO: checking out_of_order
INFO: checking system
INFO: checking solvers
INFO: checking dup_inputs
INFO: checking missing_recorders
WARNING: The Problem has no recorder of any kind attached
INFO: checking comp_has_no_outputs
INFO: checking auto_ivc_warnings
INFO: checking out_of_order
INFO: checking system
INFO: checking solvers
INFO: checking dup_inputs
INFO: checking missing_recorders
WARNING: The Problem has no recorder of any kind attached
INFO: checking comp_has_no_outputs
INFO: checking auto_ivc_warnings
Full total jacobian was computed 3 times, taking 0.540619 seconds.
Total jacobian shape: (239, 328)
Jacobian shape: (239, 328) ( 2.65% nonzero)
FWD solves: 13 REV solves: 0
Total colors vs. total size: 13 vs 328 (96.0% improvement)
Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.540619 sec.
Time to compute coloring: 0.011390 sec.
Optimization Problem -- Optimization using pyOpt_sparse
================================================================================
Objective Function: _objfunc
Solution:
--------------------------------------------------------------------------------
Total Time: 4.1756
User Objective Time : 0.0643
User Sensitivity Time : 0.5991
Interface Time : 0.8796
Opt Solver Time: 2.6326
Calls to Objective Function : 21
Calls to Sens Function : 21
Objectives
Index Name Value Optimum
0 traj.phases.phase0.indep_states.states:xL 1.673092E+00 0.000000E+00
Variables (c - continuous, i - integer, d - discrete)
Index Name Type Lower Bound Value Upper Bound Status
0 traj.phases.phase0.indep_states.states:x_0 c -1.000000E+21 1.269108E+00 1.000000E+21
1 traj.phases.phase0.indep_states.states:x_1 c -1.000000E+21 1.007417E+00 1.000000E+21
2 traj.phases.phase0.indep_states.states:x_2 c -1.000000E+21 9.363176E-01 1.000000E+21
3 traj.phases.phase0.indep_states.states:x_3 c -1.000000E+21 9.363176E-01 1.000000E+21
4 traj.phases.phase0.indep_states.states:x_4 c -1.000000E+21 7.919040E-01 1.000000E+21
5 traj.phases.phase0.indep_states.states:x_5 c -1.000000E+21 6.286634E-01 1.000000E+21
6 traj.phases.phase0.indep_states.states:x_6 c -1.000000E+21 5.843401E-01 1.000000E+21
7 traj.phases.phase0.indep_states.states:x_7 c -1.000000E+21 5.843401E-01 1.000000E+21
8 traj.phases.phase0.indep_states.states:x_8 c -1.000000E+21 4.942695E-01 1.000000E+21
9 traj.phases.phase0.indep_states.states:x_9 c -1.000000E+21 3.923746E-01 1.000000E+21
10 traj.phases.phase0.indep_states.states:x_10 c -1.000000E+21 3.646989E-01 1.000000E+21
11 traj.phases.phase0.indep_states.states:x_11 c -1.000000E+21 3.646989E-01 1.000000E+21
12 traj.phases.phase0.indep_states.states:x_12 c -1.000000E+21 3.084568E-01 1.000000E+21
13 traj.phases.phase0.indep_states.states:x_13 c -1.000000E+21 2.448452E-01 1.000000E+21
14 traj.phases.phase0.indep_states.states:x_14 c -1.000000E+21 2.275748E-01 1.000000E+21
15 traj.phases.phase0.indep_states.states:x_15 c -1.000000E+21 2.275748E-01 1.000000E+21
16 traj.phases.phase0.indep_states.states:x_16 c -1.000000E+21 1.924929E-01 1.000000E+21
17 traj.phases.phase0.indep_states.states:x_17 c -1.000000E+21 1.528237E-01 1.000000E+21
18 traj.phases.phase0.indep_states.states:x_18 c -1.000000E+21 1.420491E-01 1.000000E+21
19 traj.phases.phase0.indep_states.states:x_19 c -1.000000E+21 1.420491E-01 1.000000E+21
20 traj.phases.phase0.indep_states.states:x_20 c -1.000000E+21 1.201483E-01 1.000000E+21
21 traj.phases.phase0.indep_states.states:x_21 c -1.000000E+21 9.537271E-02 1.000000E+21
22 traj.phases.phase0.indep_states.states:x_22 c -1.000000E+21 8.864688E-02 1.000000E+21
23 traj.phases.phase0.indep_states.states:x_23 c -1.000000E+21 8.864688E-02 1.000000E+21
24 traj.phases.phase0.indep_states.states:x_24 c -1.000000E+21 7.498777E-02 1.000000E+21
25 traj.phases.phase0.indep_states.states:x_25 c -1.000000E+21 5.954783E-02 1.000000E+21
26 traj.phases.phase0.indep_states.states:x_26 c -1.000000E+21 5.535471E-02 1.000000E+21
27 traj.phases.phase0.indep_states.states:x_27 c -1.000000E+21 5.535471E-02 1.000000E+21
28 traj.phases.phase0.indep_states.states:x_28 c -1.000000E+21 4.683190E-02 1.000000E+21
29 traj.phases.phase0.indep_states.states:x_29 c -1.000000E+21 3.719119E-02 1.000000E+21
30 traj.phases.phase0.indep_states.states:x_30 c -1.000000E+21 3.457443E-02 1.000000E+21
31 traj.phases.phase0.indep_states.states:x_31 c -1.000000E+21 3.457443E-02 1.000000E+21
32 traj.phases.phase0.indep_states.states:x_32 c -1.000000E+21 2.926120E-02 1.000000E+21
33 traj.phases.phase0.indep_states.states:x_33 c -1.000000E+21 2.325785E-02 1.000000E+21
34 traj.phases.phase0.indep_states.states:x_34 c -1.000000E+21 2.162822E-02 1.000000E+21
35 traj.phases.phase0.indep_states.states:x_35 c -1.000000E+21 2.162822E-02 1.000000E+21
36 traj.phases.phase0.indep_states.states:x_36 c -1.000000E+21 1.831733E-02 1.000000E+21
37 traj.phases.phase0.indep_states.states:x_37 c -1.000000E+21 1.457560E-02 1.000000E+21
38 traj.phases.phase0.indep_states.states:x_38 c -1.000000E+21 1.356090E-02 1.000000E+21
39 traj.phases.phase0.indep_states.states:x_39 c -1.000000E+21 1.356090E-02 1.000000E+21
40 traj.phases.phase0.indep_states.states:x_40 c -1.000000E+21 1.150248E-02 1.000000E+21
41 traj.phases.phase0.indep_states.states:x_41 c -1.000000E+21 9.182136E-03 1.000000E+21
42 traj.phases.phase0.indep_states.states:x_42 c -1.000000E+21 8.553999E-03 1.000000E+21
43 traj.phases.phase0.indep_states.states:x_43 c -1.000000E+21 8.553999E-03 1.000000E+21
44 traj.phases.phase0.indep_states.states:x_44 c -1.000000E+21 7.281583E-03 1.000000E+21
45 traj.phases.phase0.indep_states.states:x_45 c -1.000000E+21 5.853477E-03 1.000000E+21
46 traj.phases.phase0.indep_states.states:x_46 c -1.000000E+21 5.469083E-03 1.000000E+21
47 traj.phases.phase0.indep_states.states:x_47 c -1.000000E+21 5.469083E-03 1.000000E+21
48 traj.phases.phase0.indep_states.states:x_48 c -1.000000E+21 4.695414E-03 1.000000E+21
49 traj.phases.phase0.indep_states.states:x_49 c -1.000000E+21 3.839906E-03 1.000000E+21
50 traj.phases.phase0.indep_states.states:x_50 c -1.000000E+21 3.613302E-03 1.000000E+21
51 traj.phases.phase0.indep_states.states:x_51 c -1.000000E+21 3.613302E-03 1.000000E+21
52 traj.phases.phase0.indep_states.states:x_52 c -1.000000E+21 3.164911E-03 1.000000E+21
53 traj.phases.phase0.indep_states.states:x_53 c -1.000000E+21 2.689883E-03 1.000000E+21
54 traj.phases.phase0.indep_states.states:x_54 c -1.000000E+21 2.570378E-03 1.000000E+21
55 traj.phases.phase0.indep_states.states:x_55 c -1.000000E+21 2.570378E-03 1.000000E+21
56 traj.phases.phase0.indep_states.states:x_56 c -1.000000E+21 2.347606E-03 1.000000E+21
57 traj.phases.phase0.indep_states.states:x_57 c -1.000000E+21 2.148626E-03 1.000000E+21
58 traj.phases.phase0.indep_states.states:x_58 c -1.000000E+21 2.110143E-03 1.000000E+21
59 traj.phases.phase0.indep_states.states:x_59 c -1.000000E+21 2.110143E-03 1.000000E+21
60 traj.phases.phase0.indep_states.states:x_60 c -1.000000E+21 2.064633E-03 1.000000E+21
61 traj.phases.phase0.indep_states.states:x_61 c -1.000000E+21 2.099164E-03 1.000000E+21
62 traj.phases.phase0.indep_states.states:x_62 c -1.000000E+21 2.133709E-03 1.000000E+21
63 traj.phases.phase0.indep_states.states:x_63 c -1.000000E+21 2.133709E-03 1.000000E+21
64 traj.phases.phase0.indep_states.states:x_64 c -1.000000E+21 2.256671E-03 1.000000E+21
65 traj.phases.phase0.indep_states.states:x_65 c -1.000000E+21 2.534272E-03 1.000000E+21
66 traj.phases.phase0.indep_states.states:x_66 c -1.000000E+21 2.650120E-03 1.000000E+21
67 traj.phases.phase0.indep_states.states:x_67 c -1.000000E+21 2.650120E-03 1.000000E+21
68 traj.phases.phase0.indep_states.states:x_68 c -1.000000E+21 2.970266E-03 1.000000E+21
69 traj.phases.phase0.indep_states.states:x_69 c -1.000000E+21 3.554724E-03 1.000000E+21
70 traj.phases.phase0.indep_states.states:x_70 c -1.000000E+21 3.778370E-03 1.000000E+21
71 traj.phases.phase0.indep_states.states:x_71 c -1.000000E+21 3.778370E-03 1.000000E+21
72 traj.phases.phase0.indep_states.states:x_72 c -1.000000E+21 4.368675E-03 1.000000E+21
73 traj.phases.phase0.indep_states.states:x_73 c -1.000000E+21 5.392046E-03 1.000000E+21
74 traj.phases.phase0.indep_states.states:x_74 c -1.000000E+21 5.773635E-03 1.000000E+21
75 traj.phases.phase0.indep_states.states:x_75 c -1.000000E+21 5.773635E-03 1.000000E+21
76 traj.phases.phase0.indep_states.states:x_76 c -1.000000E+21 6.765977E-03 1.000000E+21
77 traj.phases.phase0.indep_states.states:x_77 c -1.000000E+21 8.458060E-03 1.000000E+21
78 traj.phases.phase0.indep_states.states:x_78 c -1.000000E+21 9.084038E-03 1.000000E+21
79 traj.phases.phase0.indep_states.states:x_79 c -1.000000E+21 9.084038E-03 1.000000E+21
80 traj.phases.phase0.indep_states.states:x_80 c -1.000000E+21 1.070431E-02 1.000000E+21
81 traj.phases.phase0.indep_states.states:x_81 c -1.000000E+21 1.344760E-02 1.000000E+21
82 traj.phases.phase0.indep_states.states:x_82 c -1.000000E+21 1.445771E-02 1.000000E+21
83 traj.phases.phase0.indep_states.states:x_83 c -1.000000E+21 1.445771E-02 1.000000E+21
84 traj.phases.phase0.indep_states.states:x_84 c -1.000000E+21 1.706507E-02 1.000000E+21
85 traj.phases.phase0.indep_states.states:x_85 c -1.000000E+21 2.147356E-02 1.000000E+21
86 traj.phases.phase0.indep_states.states:x_86 c -1.000000E+21 2.309787E-02 1.000000E+21
87 traj.phases.phase0.indep_states.states:x_87 c -1.000000E+21 2.309787E-02 1.000000E+21
88 traj.phases.phase0.indep_states.states:x_88 c -1.000000E+21 2.729234E-02 1.000000E+21
89 traj.phases.phase0.indep_states.states:x_89 c -1.000000E+21 3.437077E-02 1.000000E+21
90 traj.phases.phase0.indep_states.states:x_90 c -1.000000E+21 3.697183E-02 1.000000E+21
91 traj.phases.phase0.indep_states.states:x_91 c -1.000000E+21 3.697183E-02 1.000000E+21
92 traj.phases.phase0.indep_states.states:x_92 c -1.000000E+21 4.367764E-02 1.000000E+21
93 traj.phases.phase0.indep_states.states:x_93 c -1.000000E+21 5.500533E-02 1.000000E+21
94 traj.phases.phase0.indep_states.states:x_94 c -1.000000E+21 5.917857E-02 1.000000E+21
95 traj.phases.phase0.indep_states.states:x_95 c -1.000000E+21 5.917857E-02 1.000000E+21
96 traj.phases.phase0.indep_states.states:x_96 c -1.000000E+21 6.995534E-02 1.000000E+21
97 traj.phases.phase0.indep_states.states:x_97 c -1.000000E+21 8.813445E-02 1.000000E+21
98 traj.phases.phase0.indep_states.states:x_98 c -1.000000E+21 9.481117E-02 1.000000E+21
99 traj.phases.phase0.indep_states.states:x_99 c -1.000000E+21 9.481117E-02 1.000000E+21
100 traj.phases.phase0.indep_states.states:x_100 c -1.000000E+21 1.120185E-01 1.000000E+21
101 traj.phases.phase0.indep_states.states:x_101 c -1.000000E+21 1.410841E-01 1.000000E+21
102 traj.phases.phase0.indep_states.states:x_102 c -1.000000E+21 1.517946E-01 1.000000E+21
103 traj.phases.phase0.indep_states.states:x_103 c -1.000000E+21 1.517946E-01 1.000000E+21
104 traj.phases.phase0.indep_states.states:x_104 c -1.000000E+21 1.794583E-01 1.000000E+21
105 traj.phases.phase0.indep_states.states:x_105 c -1.000000E+21 2.261255E-01 1.000000E+21
106 traj.phases.phase0.indep_states.states:x_106 c -1.000000E+21 2.432632E-01 1.000000E+21
107 traj.phases.phase0.indep_states.states:x_107 c -1.000000E+21 2.432632E-01 1.000000E+21
108 traj.phases.phase0.indep_states.states:x_108 c -1.000000E+21 2.874253E-01 1.000000E+21
109 traj.phases.phase0.indep_states.states:x_109 c -1.000000E+21 3.620125E-01 1.000000E+21
110 traj.phases.phase0.indep_states.states:x_110 c -1.000000E+21 3.894965E-01 1.000000E+21
111 traj.phases.phase0.indep_states.states:x_111 c -1.000000E+21 3.894965E-01 1.000000E+21
112 traj.phases.phase0.indep_states.states:x_112 c -1.000000E+21 4.604895E-01 1.000000E+21
113 traj.phases.phase0.indep_states.states:x_113 c -1.000000E+21 5.803120E-01 1.000000E+21
114 traj.phases.phase0.indep_states.states:x_114 c -1.000000E+21 6.243383E-01 1.000000E+21
115 traj.phases.phase0.indep_states.states:x_115 c -1.000000E+21 6.243383E-01 1.000000E+21
116 traj.phases.phase0.indep_states.states:x_116 c -1.000000E+21 7.378232E-01 1.000000E+21
117 traj.phases.phase0.indep_states.states:x_117 c -1.000000E+21 9.294362E-01 1.000000E+21
118 traj.phases.phase0.indep_states.states:x_118 c -1.000000E+21 1.000000E+00 1.000000E+21
119 traj.phases.phase0.indep_states.states:xL_0 c -1.000000E+21 1.326004E-01 1.000000E+21
120 traj.phases.phase0.indep_states.states:xL_1 c -1.000000E+21 2.555825E-01 1.000000E+21
121 traj.phases.phase0.indep_states.states:xL_2 c -1.000000E+21 2.844232E-01 1.000000E+21
122 traj.phases.phase0.indep_states.states:xL_3 c -1.000000E+21 2.844232E-01 1.000000E+21
123 traj.phases.phase0.indep_states.states:xL_4 c -1.000000E+21 3.361881E-01 1.000000E+21
124 traj.phases.phase0.indep_states.states:xL_5 c -1.000000E+21 3.840500E-01 1.000000E+21
125 traj.phases.phase0.indep_states.states:xL_6 c -1.000000E+21 3.952749E-01 1.000000E+21
126 traj.phases.phase0.indep_states.states:xL_7 c -1.000000E+21 3.952749E-01 1.000000E+21
127 traj.phases.phase0.indep_states.states:xL_8 c -1.000000E+21 4.154245E-01 1.000000E+21
128 traj.phases.phase0.indep_states.states:xL_9 c -1.000000E+21 4.340720E-01 1.000000E+21
129 traj.phases.phase0.indep_states.states:xL_10 c -1.000000E+21 4.384460E-01 1.000000E+21
130 traj.phases.phase0.indep_states.states:xL_11 c -1.000000E+21 4.384460E-01 1.000000E+21
131 traj.phases.phase0.indep_states.states:xL_12 c -1.000000E+21 4.462983E-01 1.000000E+21
132 traj.phases.phase0.indep_states.states:xL_13 c -1.000000E+21 4.535630E-01 1.000000E+21
133 traj.phases.phase0.indep_states.states:xL_14 c -1.000000E+21 4.552663E-01 1.000000E+21
134 traj.phases.phase0.indep_states.states:xL_15 c -1.000000E+21 4.552663E-01 1.000000E+21
135 traj.phases.phase0.indep_states.states:xL_16 c -1.000000E+21 4.583228E-01 1.000000E+21
136 traj.phases.phase0.indep_states.states:xL_17 c -1.000000E+21 4.611501E-01 1.000000E+21
137 traj.phases.phase0.indep_states.states:xL_18 c -1.000000E+21 4.618134E-01 1.000000E+21
138 traj.phases.phase0.indep_states.states:xL_19 c -1.000000E+21 4.618134E-01 1.000000E+21
139 traj.phases.phase0.indep_states.states:xL_20 c -1.000000E+21 4.630044E-01 1.000000E+21
140 traj.phases.phase0.indep_states.states:xL_21 c -1.000000E+21 4.641065E-01 1.000000E+21
141 traj.phases.phase0.indep_states.states:xL_22 c -1.000000E+21 4.643649E-01 1.000000E+21
142 traj.phases.phase0.indep_states.states:xL_23 c -1.000000E+21 4.643649E-01 1.000000E+21
143 traj.phases.phase0.indep_states.states:xL_24 c -1.000000E+21 4.648285E-01 1.000000E+21
144 traj.phases.phase0.indep_states.states:xL_25 c -1.000000E+21 4.652572E-01 1.000000E+21
145 traj.phases.phase0.indep_states.states:xL_26 c -1.000000E+21 4.653578E-01 1.000000E+21
146 traj.phases.phase0.indep_states.states:xL_27 c -1.000000E+21 4.653578E-01 1.000000E+21
147 traj.phases.phase0.indep_states.states:xL_28 c -1.000000E+21 4.655384E-01 1.000000E+21
148 traj.phases.phase0.indep_states.states:xL_29 c -1.000000E+21 4.657056E-01 1.000000E+21
149 traj.phases.phase0.indep_states.states:xL_30 c -1.000000E+21 4.657448E-01 1.000000E+21
150 traj.phases.phase0.indep_states.states:xL_31 c -1.000000E+21 4.657448E-01 1.000000E+21
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327 traj.phases.phase0.control_group.indep_controls.controls:u_89 c -1.000000E+21 2.245279E+00 1.000000E+21
Constraints (i - inequality, e - equality)
Index Name Type Lower Value Upper Status Lagrange Multiplier (N/A)
0 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 7.401487E-17 0.000000E+00 9.00000E+100
1 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -3.700743E-17 0.000000E+00 9.00000E+100
2 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -3.700743E-17 0.000000E+00 9.00000E+100
3 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 3.700743E-17 0.000000E+00 9.00000E+100
4 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
5 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 1.850372E-17 0.000000E+00 9.00000E+100
6 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -7.401487E-17 0.000000E+00 9.00000E+100
7 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 1.850372E-17 0.000000E+00 9.00000E+100
8 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -1.480297E-16 0.000000E+00 9.00000E+100
9 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -7.401487E-17 0.000000E+00 9.00000E+100
10 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 4.625929E-17 0.000000E+00 9.00000E+100
11 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 1.017704E-16 0.000000E+00 9.00000E+100
12 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -4.625929E-17 0.000000E+00 9.00000E+100
13 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 5.551115E-17 0.000000E+00 9.00000E+100
14 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -5.551115E-17 0.000000E+00 9.00000E+100
15 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 4.625929E-17 0.000000E+00 9.00000E+100
16 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
17 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 4.163336E-17 0.000000E+00 9.00000E+100
18 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -2.312965E-17 0.000000E+00 9.00000E+100
19 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -1.387779E-17 0.000000E+00 9.00000E+100
20 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -2.312965E-18 0.000000E+00 9.00000E+100
21 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -4.394633E-17 0.000000E+00 9.00000E+100
22 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -6.938894E-18 0.000000E+00 9.00000E+100
23 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -1.156482E-17 0.000000E+00 9.00000E+100
24 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -1.040834E-17 0.000000E+00 9.00000E+100
25 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -6.938894E-18 0.000000E+00 9.00000E+100
26 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 5.782412E-18 0.000000E+00 9.00000E+100
27 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -9.251859E-18 0.000000E+00 9.00000E+100
28 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -5.782412E-19 0.000000E+00 9.00000E+100
29 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -3.469447E-18 0.000000E+00 9.00000E+100
30 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 4.047688E-18 0.000000E+00 9.00000E+100
31 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -1.734723E-18 0.000000E+00 9.00000E+100
32 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -2.891206E-18 0.000000E+00 9.00000E+100
33 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -5.204170E-18 0.000000E+00 9.00000E+100
34 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 5.782412E-19 0.000000E+00 9.00000E+100
35 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 1.011922E-18 0.000000E+00 9.00000E+100
36 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -1.156482E-18 0.000000E+00 9.00000E+100
37 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
38 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 7.228014E-19 0.000000E+00 9.00000E+100
39 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 1.011922E-18 0.000000E+00 9.00000E+100
40 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -2.891206E-19 0.000000E+00 9.00000E+100
41 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -7.228014E-20 0.000000E+00 9.00000E+100
42 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -1.084202E-18 0.000000E+00 9.00000E+100
43 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 3.975408E-19 0.000000E+00 9.00000E+100
44 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 5.421011E-19 0.000000E+00 9.00000E+100
45 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -6.324513E-19 0.000000E+00 9.00000E+100
46 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -4.517509E-21 0.000000E+00 9.00000E+100
47 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 6.685913E-19 0.000000E+00 9.00000E+100
48 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 2.638225E-18 0.000000E+00 9.00000E+100
49 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 1.807004E-19 0.000000E+00 9.00000E+100
50 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 7.228014E-20 0.000000E+00 9.00000E+100
51 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -1.445603E-19 0.000000E+00 9.00000E+100
52 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 5.782412E-19 0.000000E+00 9.00000E+100
53 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -1.590163E-18 0.000000E+00 9.00000E+100
54 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -1.301043E-18 0.000000E+00 9.00000E+100
55 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 1.445603E-19 0.000000E+00 9.00000E+100
56 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -1.156482E-18 0.000000E+00 9.00000E+100
57 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 2.891206E-19 0.000000E+00 9.00000E+100
58 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -2.023844E-18 0.000000E+00 9.00000E+100
59 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 8.673617E-19 0.000000E+00 9.00000E+100
60 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
61 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 4.336809E-18 0.000000E+00 9.00000E+100
62 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -2.891206E-18 0.000000E+00 9.00000E+100
63 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 9.830100E-18 0.000000E+00 9.00000E+100
64 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -2.312965E-18 0.000000E+00 9.00000E+100
65 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 1.156482E-18 0.000000E+00 9.00000E+100
66 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 3.122502E-17 0.000000E+00 9.00000E+100
67 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -3.469447E-18 0.000000E+00 9.00000E+100
68 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 9.251859E-18 0.000000E+00 9.00000E+100
69 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 4.625929E-18 0.000000E+00 9.00000E+100
70 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -8.095376E-18 0.000000E+00 9.00000E+100
71 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -6.938894E-18 0.000000E+00 9.00000E+100
72 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -3.700743E-17 0.000000E+00 9.00000E+100
73 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -4.625929E-17 0.000000E+00 9.00000E+100
74 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 5.782412E-17 0.000000E+00 9.00000E+100
75 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -5.551115E-17 0.000000E+00 9.00000E+100
76 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 2.775558E-17 0.000000E+00 9.00000E+100
77 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 2.775558E-17 0.000000E+00 9.00000E+100
78 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -1.526557E-16 0.000000E+00 9.00000E+100
79 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 4.625929E-17 0.000000E+00 9.00000E+100
80 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -2.775558E-17 0.000000E+00 9.00000E+100
81 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -1.202742E-16 0.000000E+00 9.00000E+100
82 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 1.017704E-16 0.000000E+00 9.00000E+100
83 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -2.035409E-16 0.000000E+00 9.00000E+100
84 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 3.700743E-17 0.000000E+00 9.00000E+100
85 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 3.700743E-17 0.000000E+00 9.00000E+100
86 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 1.480297E-16 0.000000E+00 9.00000E+100
87 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -3.700743E-17 0.000000E+00 9.00000E+100
88 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -3.700743E-17 0.000000E+00 9.00000E+100
89 traj.phases.phase0.collocation_constraint.defects:x e 0.000000E+00 -1.110223E-16 0.000000E+00 9.00000E+100
90 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -3.263776E-08 0.000000E+00 9.00000E+100
91 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -2.767390E-09 0.000000E+00 9.00000E+100
92 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -3.060948E-08 0.000000E+00 9.00000E+100
93 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -2.766599E-08 0.000000E+00 9.00000E+100
94 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.687911E-08 0.000000E+00 9.00000E+100
95 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.163169E-08 0.000000E+00 9.00000E+100
96 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.146235E-08 0.000000E+00 9.00000E+100
97 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.170814E-08 0.000000E+00 9.00000E+100
98 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.184551E-08 0.000000E+00 9.00000E+100
99 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.183684E-08 0.000000E+00 9.00000E+100
100 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.132005E-08 0.000000E+00 9.00000E+100
101 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -9.241620E-09 0.000000E+00 9.00000E+100
102 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -8.342387E-09 0.000000E+00 9.00000E+100
103 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -6.569790E-09 0.000000E+00 9.00000E+100
104 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -5.030081E-09 0.000000E+00 9.00000E+100
105 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -4.701198E-09 0.000000E+00 9.00000E+100
106 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -3.921658E-09 0.000000E+00 9.00000E+100
107 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -2.727725E-09 0.000000E+00 9.00000E+100
108 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -2.409630E-09 0.000000E+00 9.00000E+100
109 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.955672E-09 0.000000E+00 9.00000E+100
110 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.725085E-09 0.000000E+00 9.00000E+100
111 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.688025E-09 0.000000E+00 9.00000E+100
112 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.741365E-09 0.000000E+00 9.00000E+100
113 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -2.344934E-09 0.000000E+00 9.00000E+100
114 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -2.692930E-09 0.000000E+00 9.00000E+100
115 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -3.617070E-09 0.000000E+00 9.00000E+100
116 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -4.847928E-09 0.000000E+00 9.00000E+100
117 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -5.191017E-09 0.000000E+00 9.00000E+100
118 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -6.020417E-09 0.000000E+00 9.00000E+100
119 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -7.421865E-09 0.000000E+00 9.00000E+100
120 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -7.926399E-09 0.000000E+00 9.00000E+100
121 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -9.070646E-09 0.000000E+00 9.00000E+100
122 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.044615E-08 0.000000E+00 9.00000E+100
123 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.081695E-08 0.000000E+00 9.00000E+100
124 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.162814E-08 0.000000E+00 9.00000E+100
125 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.274202E-08 0.000000E+00 9.00000E+100
126 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.309022E-08 0.000000E+00 9.00000E+100
127 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.383392E-08 0.000000E+00 9.00000E+100
128 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.467756E-08 0.000000E+00 9.00000E+100
129 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.489593E-08 0.000000E+00 9.00000E+100
130 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.534432E-08 0.000000E+00 9.00000E+100
131 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.588387E-08 0.000000E+00 9.00000E+100
132 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.603538E-08 0.000000E+00 9.00000E+100
133 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.633161E-08 0.000000E+00 9.00000E+100
134 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.660682E-08 0.000000E+00 9.00000E+100
135 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.666123E-08 0.000000E+00 9.00000E+100
136 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.674957E-08 0.000000E+00 9.00000E+100
137 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.681608E-08 0.000000E+00 9.00000E+100
138 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.682510E-08 0.000000E+00 9.00000E+100
139 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.680275E-08 0.000000E+00 9.00000E+100
140 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.665136E-08 0.000000E+00 9.00000E+100
141 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.657442E-08 0.000000E+00 9.00000E+100
142 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.638733E-08 0.000000E+00 9.00000E+100
143 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.615335E-08 0.000000E+00 9.00000E+100
144 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.608750E-08 0.000000E+00 9.00000E+100
145 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.588222E-08 0.000000E+00 9.00000E+100
146 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.539718E-08 0.000000E+00 9.00000E+100
147 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.519373E-08 0.000000E+00 9.00000E+100
148 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.475653E-08 0.000000E+00 9.00000E+100
149 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.435172E-08 0.000000E+00 9.00000E+100
150 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.427656E-08 0.000000E+00 9.00000E+100
151 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.399350E-08 0.000000E+00 9.00000E+100
152 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.311850E-08 0.000000E+00 9.00000E+100
153 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.272396E-08 0.000000E+00 9.00000E+100
154 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.193357E-08 0.000000E+00 9.00000E+100
155 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.142825E-08 0.000000E+00 9.00000E+100
156 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.142197E-08 0.000000E+00 9.00000E+100
157 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.117655E-08 0.000000E+00 9.00000E+100
158 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -9.749678E-09 0.000000E+00 9.00000E+100
159 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -9.063779E-09 0.000000E+00 9.00000E+100
160 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -7.797875E-09 0.000000E+00 9.00000E+100
161 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -7.243868E-09 0.000000E+00 9.00000E+100
162 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -7.387185E-09 0.000000E+00 9.00000E+100
163 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -7.382258E-09 0.000000E+00 9.00000E+100
164 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -5.534376E-09 0.000000E+00 9.00000E+100
165 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -4.701175E-09 0.000000E+00 9.00000E+100
166 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -3.455361E-09 0.000000E+00 9.00000E+100
167 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -2.791335E-09 0.000000E+00 9.00000E+100
168 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -2.924310E-09 0.000000E+00 9.00000E+100
169 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -3.265419E-09 0.000000E+00 9.00000E+100
170 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.991133E-09 0.000000E+00 9.00000E+100
171 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.751690E-09 0.000000E+00 9.00000E+100
172 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -2.301217E-09 0.000000E+00 9.00000E+100
173 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.202696E-09 0.000000E+00 9.00000E+100
174 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -6.034656E-10 0.000000E+00 9.00000E+100
175 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -5.319636E-10 0.000000E+00 9.00000E+100
176 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -3.565547E-10 0.000000E+00 9.00000E+100
177 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -8.051677E-10 0.000000E+00 9.00000E+100
178 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -2.797383E-09 0.000000E+00 9.00000E+100
179 traj.phases.phase0.collocation_constraint.defects:xL e 0.000000E+00 -1.097801E-09 0.000000E+00 9.00000E+100
180 traj.phases.phase0.continuity_comp.defect_states:x e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
181 traj.phases.phase0.continuity_comp.defect_states:x e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
182 traj.phases.phase0.continuity_comp.defect_states:x e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
183 traj.phases.phase0.continuity_comp.defect_states:x e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
184 traj.phases.phase0.continuity_comp.defect_states:x e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
185 traj.phases.phase0.continuity_comp.defect_states:x e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
186 traj.phases.phase0.continuity_comp.defect_states:x e 0.000000E+00 -6.938894E-18 0.000000E+00 9.00000E+100
187 traj.phases.phase0.continuity_comp.defect_states:x e 0.000000E+00 6.938894E-18 0.000000E+00 9.00000E+100
188 traj.phases.phase0.continuity_comp.defect_states:x e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
189 traj.phases.phase0.continuity_comp.defect_states:x e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
190 traj.phases.phase0.continuity_comp.defect_states:x e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
191 traj.phases.phase0.continuity_comp.defect_states:x e 0.000000E+00 8.673617E-19 0.000000E+00 9.00000E+100
192 traj.phases.phase0.continuity_comp.defect_states:x e 0.000000E+00 4.336809E-19 0.000000E+00 9.00000E+100
193 traj.phases.phase0.continuity_comp.defect_states:x e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
194 traj.phases.phase0.continuity_comp.defect_states:x e 0.000000E+00 4.336809E-19 0.000000E+00 9.00000E+100
195 traj.phases.phase0.continuity_comp.defect_states:x e 0.000000E+00 4.336809E-19 0.000000E+00 9.00000E+100
196 traj.phases.phase0.continuity_comp.defect_states:x e 0.000000E+00 4.336809E-19 0.000000E+00 9.00000E+100
197 traj.phases.phase0.continuity_comp.defect_states:x e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
198 traj.phases.phase0.continuity_comp.defect_states:x e 0.000000E+00 8.673617E-19 0.000000E+00 9.00000E+100
199 traj.phases.phase0.continuity_comp.defect_states:x e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
200 traj.phases.phase0.continuity_comp.defect_states:x e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
201 traj.phases.phase0.continuity_comp.defect_states:x e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
202 traj.phases.phase0.continuity_comp.defect_states:x e 0.000000E+00 -6.938894E-18 0.000000E+00 9.00000E+100
203 traj.phases.phase0.continuity_comp.defect_states:x e 0.000000E+00 -6.938894E-18 0.000000E+00 9.00000E+100
204 traj.phases.phase0.continuity_comp.defect_states:x e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
205 traj.phases.phase0.continuity_comp.defect_states:x e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
206 traj.phases.phase0.continuity_comp.defect_states:x e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
207 traj.phases.phase0.continuity_comp.defect_states:x e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
208 traj.phases.phase0.continuity_comp.defect_states:x e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
209 traj.phases.phase0.continuity_comp.defect_states:xL e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
210 traj.phases.phase0.continuity_comp.defect_states:xL e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
211 traj.phases.phase0.continuity_comp.defect_states:xL e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
212 traj.phases.phase0.continuity_comp.defect_states:xL e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
213 traj.phases.phase0.continuity_comp.defect_states:xL e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
214 traj.phases.phase0.continuity_comp.defect_states:xL e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
215 traj.phases.phase0.continuity_comp.defect_states:xL e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
216 traj.phases.phase0.continuity_comp.defect_states:xL e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
217 traj.phases.phase0.continuity_comp.defect_states:xL e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
218 traj.phases.phase0.continuity_comp.defect_states:xL e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
219 traj.phases.phase0.continuity_comp.defect_states:xL e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
220 traj.phases.phase0.continuity_comp.defect_states:xL e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
221 traj.phases.phase0.continuity_comp.defect_states:xL e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
222 traj.phases.phase0.continuity_comp.defect_states:xL e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
223 traj.phases.phase0.continuity_comp.defect_states:xL e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
224 traj.phases.phase0.continuity_comp.defect_states:xL e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
225 traj.phases.phase0.continuity_comp.defect_states:xL e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
226 traj.phases.phase0.continuity_comp.defect_states:xL e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
227 traj.phases.phase0.continuity_comp.defect_states:xL e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
228 traj.phases.phase0.continuity_comp.defect_states:xL e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
229 traj.phases.phase0.continuity_comp.defect_states:xL e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
230 traj.phases.phase0.continuity_comp.defect_states:xL e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
231 traj.phases.phase0.continuity_comp.defect_states:xL e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
232 traj.phases.phase0.continuity_comp.defect_states:xL e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
233 traj.phases.phase0.continuity_comp.defect_states:xL e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
234 traj.phases.phase0.continuity_comp.defect_states:xL e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
235 traj.phases.phase0.continuity_comp.defect_states:xL e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
236 traj.phases.phase0.continuity_comp.defect_states:xL e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
237 traj.phases.phase0.continuity_comp.defect_states:xL e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
238 traj.phases.phase0.continuity_comp.defect_controls:u e 0.000000E+00 5.551115E-17 0.000000E+00 9.00000E+100
239 traj.phases.phase0.continuity_comp.defect_controls:u e 0.000000E+00 -5.551115E-17 0.000000E+00 9.00000E+100
240 traj.phases.phase0.continuity_comp.defect_controls:u e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
241 traj.phases.phase0.continuity_comp.defect_controls:u e 0.000000E+00 -1.387779E-17 0.000000E+00 9.00000E+100
242 traj.phases.phase0.continuity_comp.defect_controls:u e 0.000000E+00 -1.387779E-17 0.000000E+00 9.00000E+100
243 traj.phases.phase0.continuity_comp.defect_controls:u e 0.000000E+00 -6.938894E-18 0.000000E+00 9.00000E+100
244 traj.phases.phase0.continuity_comp.defect_controls:u e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
245 traj.phases.phase0.continuity_comp.defect_controls:u e 0.000000E+00 -1.734723E-18 0.000000E+00 9.00000E+100
246 traj.phases.phase0.continuity_comp.defect_controls:u e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
247 traj.phases.phase0.continuity_comp.defect_controls:u e 0.000000E+00 8.673617E-19 0.000000E+00 9.00000E+100
248 traj.phases.phase0.continuity_comp.defect_controls:u e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
249 traj.phases.phase0.continuity_comp.defect_controls:u e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
250 traj.phases.phase0.continuity_comp.defect_controls:u e 0.000000E+00 -2.168404E-19 0.000000E+00 9.00000E+100
251 traj.phases.phase0.continuity_comp.defect_controls:u e 0.000000E+00 -1.626303E-19 0.000000E+00 9.00000E+100
252 traj.phases.phase0.continuity_comp.defect_controls:u e 0.000000E+00 6.505213E-19 0.000000E+00 9.00000E+100
253 traj.phases.phase0.continuity_comp.defect_controls:u e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
254 traj.phases.phase0.continuity_comp.defect_controls:u e 0.000000E+00 8.673617E-19 0.000000E+00 9.00000E+100
255 traj.phases.phase0.continuity_comp.defect_controls:u e 0.000000E+00 -1.734723E-18 0.000000E+00 9.00000E+100
256 traj.phases.phase0.continuity_comp.defect_controls:u e 0.000000E+00 1.734723E-18 0.000000E+00 9.00000E+100
257 traj.phases.phase0.continuity_comp.defect_controls:u e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
258 traj.phases.phase0.continuity_comp.defect_controls:u e 0.000000E+00 6.938894E-18 0.000000E+00 9.00000E+100
259 traj.phases.phase0.continuity_comp.defect_controls:u e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
260 traj.phases.phase0.continuity_comp.defect_controls:u e 0.000000E+00 1.387779E-17 0.000000E+00 9.00000E+100
261 traj.phases.phase0.continuity_comp.defect_controls:u e 0.000000E+00 -2.775558E-17 0.000000E+00 9.00000E+100
262 traj.phases.phase0.continuity_comp.defect_controls:u e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
263 traj.phases.phase0.continuity_comp.defect_controls:u e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
264 traj.phases.phase0.continuity_comp.defect_controls:u e 0.000000E+00 1.110223E-16 0.000000E+00 9.00000E+100
265 traj.phases.phase0.continuity_comp.defect_controls:u e 0.000000E+00 1.110223E-16 0.000000E+00 9.00000E+100
266 traj.phases.phase0.continuity_comp.defect_controls:u e 0.000000E+00 -6.661338E-16 0.000000E+00 9.00000E+100
267 traj.phases.phase0.continuity_comp.defect_control_rates:u_rate e 0.000000E+00 9.992007E-15 0.000000E+00 9.00000E+100
268 traj.phases.phase0.continuity_comp.defect_control_rates:u_rate e 0.000000E+00 -4.996004E-15 0.000000E+00 9.00000E+100
269 traj.phases.phase0.continuity_comp.defect_control_rates:u_rate e 0.000000E+00 -3.330669E-15 0.000000E+00 9.00000E+100
270 traj.phases.phase0.continuity_comp.defect_control_rates:u_rate e 0.000000E+00 -8.326673E-16 0.000000E+00 9.00000E+100
271 traj.phases.phase0.continuity_comp.defect_control_rates:u_rate e 0.000000E+00 -1.457168E-15 0.000000E+00 9.00000E+100
272 traj.phases.phase0.continuity_comp.defect_control_rates:u_rate e 0.000000E+00 -3.816392E-16 0.000000E+00 9.00000E+100
273 traj.phases.phase0.continuity_comp.defect_control_rates:u_rate e 0.000000E+00 -2.081668E-16 0.000000E+00 9.00000E+100
274 traj.phases.phase0.continuity_comp.defect_control_rates:u_rate e 0.000000E+00 -2.081668E-16 0.000000E+00 9.00000E+100
275 traj.phases.phase0.continuity_comp.defect_control_rates:u_rate e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
276 traj.phases.phase0.continuity_comp.defect_control_rates:u_rate e 0.000000E+00 -5.204170E-17 0.000000E+00 9.00000E+100
277 traj.phases.phase0.continuity_comp.defect_control_rates:u_rate e 0.000000E+00 -1.734723E-17 0.000000E+00 9.00000E+100
278 traj.phases.phase0.continuity_comp.defect_control_rates:u_rate e 0.000000E+00 4.336809E-18 0.000000E+00 9.00000E+100
279 traj.phases.phase0.continuity_comp.defect_control_rates:u_rate e 0.000000E+00 -1.951564E-17 0.000000E+00 9.00000E+100
280 traj.phases.phase0.continuity_comp.defect_control_rates:u_rate e 0.000000E+00 -6.938894E-17 0.000000E+00 9.00000E+100
281 traj.phases.phase0.continuity_comp.defect_control_rates:u_rate e 0.000000E+00 3.035766E-17 0.000000E+00 9.00000E+100
282 traj.phases.phase0.continuity_comp.defect_control_rates:u_rate e 0.000000E+00 -1.301043E-17 0.000000E+00 9.00000E+100
283 traj.phases.phase0.continuity_comp.defect_control_rates:u_rate e 0.000000E+00 -7.806256E-17 0.000000E+00 9.00000E+100
284 traj.phases.phase0.continuity_comp.defect_control_rates:u_rate e 0.000000E+00 7.806256E-17 0.000000E+00 9.00000E+100
285 traj.phases.phase0.continuity_comp.defect_control_rates:u_rate e 0.000000E+00 3.642919E-16 0.000000E+00 9.00000E+100
286 traj.phases.phase0.continuity_comp.defect_control_rates:u_rate e 0.000000E+00 3.122502E-16 0.000000E+00 9.00000E+100
287 traj.phases.phase0.continuity_comp.defect_control_rates:u_rate e 0.000000E+00 2.081668E-16 0.000000E+00 9.00000E+100
288 traj.phases.phase0.continuity_comp.defect_control_rates:u_rate e 0.000000E+00 -2.081668E-16 0.000000E+00 9.00000E+100
289 traj.phases.phase0.continuity_comp.defect_control_rates:u_rate e 0.000000E+00 -4.163336E-16 0.000000E+00 9.00000E+100
290 traj.phases.phase0.continuity_comp.defect_control_rates:u_rate e 0.000000E+00 2.498002E-15 0.000000E+00 9.00000E+100
291 traj.phases.phase0.continuity_comp.defect_control_rates:u_rate e 0.000000E+00 2.498002E-15 0.000000E+00 9.00000E+100
292 traj.phases.phase0.continuity_comp.defect_control_rates:u_rate e 0.000000E+00 1.665335E-15 0.000000E+00 9.00000E+100
293 traj.phases.phase0.continuity_comp.defect_control_rates:u_rate e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
294 traj.phases.phase0.continuity_comp.defect_control_rates:u_rate e 0.000000E+00 -3.330669E-15 0.000000E+00 9.00000E+100
295 traj.phases.phase0.continuity_comp.defect_control_rates:u_rate e 0.000000E+00 -6.661338E-15 0.000000E+00 9.00000E+100
296 traj.phases.phase0.final_boundary_constraints.final_value:x e 1.000000E+00 1.000000E+00 1.000000E+00 9.00000E+100
--------------------------------------------------------------------------------
Simulating trajectory traj
Done simulating trajectory traj
References¶
-
Michael A Patterson, William W Hager, and Anil V Rao. A ph mesh refinement method for optimal control. Optimal Control Applications and Methods, 364:398–421, 2015. ↩