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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:

\begin{align} J &= \frac{1}{2} \int_{0}^{t_f} (x^2 + u^2) dt \end{align}

The system is subject to the dynamic constraints:

\begin{align} \frac{dx}{dt} &= -x + u \end{align}

The boundary conditions are:

\begin{align} x(t_0) &= 1.5 \\ x(t_f) &= 1 \end{align}

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:

\begin{align} x^*(t) &= c_1 e^{\sqrt{2} t} + c_2 e^{-\sqrt{2} t} \\ u^*(t) &= \dot{x}^*(t) + x^*(t) \end{align}

where:

\begin{align} c_1 &= \frac{1.5 e^{-\sqrt{2} t_f} - 1}{e^{-\sqrt{2} t_f} - e^{\sqrt{2} t_f}} \\ c_2 &= \frac{1 - 1.5 e^{\sqrt{2} t_f}}{e^{-\sqrt{2} t_f} - e^{\sqrt{2} t_f}} \end{align}

The ODE System: hyper_sensitive_ode.py

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import numpy as np
import openmdao.api as om


class HyperSensitiveODE(om.ExplicitComponent):
    states = {'x': {'rate_source': 'x_dot'},
              'xL': {'rate_source': 'L'}}

    parameters = {'u': {'targets': 'u'}}

    def initialize(self):
        self.options.declare('num_nodes', types=int)

    def setup(self):
        nn = self.options['num_nodes']

        # inputs
        self.add_input('x', val=np.zeros(nn), desc='state')
        self.add_input('xL', val=np.zeros(nn), desc='cost_state')

        self.add_input('u', val=np.zeros(nn), desc='control')

        self.add_output('x_dot', val=np.zeros(nn), desc='state rate', units='1/s')
        self.add_output('L', val=np.zeros(nn), desc='Lagrangian', units='1/s')

        # Setup partials
        self.declare_partials(of='x_dot', wrt='x', rows=np.arange(nn), cols=np.arange(nn), val=-1)
        self.declare_partials(of='x_dot', wrt='u', rows=np.arange(nn), cols=np.arange(nn), val=1)

        self.declare_partials(of='L', wrt='x', rows=np.arange(nn), cols=np.arange(nn))
        self.declare_partials(of='L', wrt='u', rows=np.arange(nn), cols=np.arange(nn))

    def compute(self, inputs, outputs):
        x = inputs['x']
        u = inputs['u']

        outputs['x_dot'] = -x + u
        outputs['L'] = (x ** 2 + u ** 2) / 2

    def compute_partials(self, inputs, jacobian):
        x = inputs['x']
        u = inputs['u']

        jacobian['L', 'x'] = x
        jacobian['L', 'u'] = u

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           
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        266  traj.phases.phase0.control_group.indep_controls.controls:u_28      c    -1.000000E+21    -7.373571E-03     1.000000E+21           
        267  traj.phases.phase0.control_group.indep_controls.controls:u_29      c    -1.000000E+21    -5.777189E-03     1.000000E+21           
        268  traj.phases.phase0.control_group.indep_controls.controls:u_30      c    -1.000000E+21    -5.343626E-03     1.000000E+21           
        269  traj.phases.phase0.control_group.indep_controls.controls:u_31      c    -1.000000E+21    -4.451478E-03     1.000000E+21           
        270  traj.phases.phase0.control_group.indep_controls.controls:u_32      c    -1.000000E+21    -3.421460E-03     1.000000E+21           
        271  traj.phases.phase0.control_group.indep_controls.controls:u_33      c    -1.000000E+21    -3.144013E-03     1.000000E+21           
        272  traj.phases.phase0.control_group.indep_controls.controls:u_34      c    -1.000000E+21    -2.566566E-03     1.000000E+21           
        273  traj.phases.phase0.control_group.indep_controls.controls:u_35      c    -1.000000E+21    -1.872104E-03     1.000000E+21           
        274  traj.phases.phase0.control_group.indep_controls.controls:u_36      c    -1.000000E+21    -1.677022E-03     1.000000E+21           
        275  traj.phases.phase0.control_group.indep_controls.controls:u_37      c    -1.000000E+21    -1.259372E-03     1.000000E+21           
        276  traj.phases.phase0.control_group.indep_controls.controls:u_38      c    -1.000000E+21    -7.338779E-04     1.000000E+21           
        277  traj.phases.phase0.control_group.indep_controls.controls:u_39      c    -1.000000E+21    -5.798275E-04     1.000000E+21           
        278  traj.phases.phase0.control_group.indep_controls.controls:u_40      c    -1.000000E+21    -2.339256E-04     1.000000E+21           
        279  traj.phases.phase0.control_group.indep_controls.controls:u_41      c    -1.000000E+21     2.430049E-04     1.000000E+21           
        280  traj.phases.phase0.control_group.indep_controls.controls:u_42      c    -1.000000E+21     3.938687E-04     1.000000E+21           
        281  traj.phases.phase0.control_group.indep_controls.controls:u_43      c    -1.000000E+21     7.530724E-04     1.000000E+21           
        282  traj.phases.phase0.control_group.indep_controls.controls:u_44      c    -1.000000E+21     1.293971E-03     1.000000E+21           
        283  traj.phases.phase0.control_group.indep_controls.controls:u_45      c    -1.000000E+21     1.476099E-03     1.000000E+21           
        284  traj.phases.phase0.control_group.indep_controls.controls:u_46      c    -1.000000E+21     1.929993E-03     1.000000E+21           
        285  traj.phases.phase0.control_group.indep_controls.controls:u_47      c    -1.000000E+21     2.657466E-03     1.000000E+21           
        286  traj.phases.phase0.control_group.indep_controls.controls:u_48      c    -1.000000E+21     2.912154E-03     1.000000E+21           
        287  traj.phases.phase0.control_group.indep_controls.controls:u_49      c    -1.000000E+21     3.563403E-03     1.000000E+21           
        288  traj.phases.phase0.control_group.indep_controls.controls:u_50      c    -1.000000E+21     4.641214E-03     1.000000E+21           
        289  traj.phases.phase0.control_group.indep_controls.controls:u_51      c    -1.000000E+21     5.025634E-03     1.000000E+21           
        290  traj.phases.phase0.control_group.indep_controls.controls:u_52      c    -1.000000E+21     6.020735E-03     1.000000E+21           
        291  traj.phases.phase0.control_group.indep_controls.controls:u_53      c    -1.000000E+21     7.692526E-03     1.000000E+21           
        292  traj.phases.phase0.control_group.indep_controls.controls:u_54      c    -1.000000E+21     8.293816E-03     1.000000E+21           
        293  traj.phases.phase0.control_group.indep_controls.controls:u_55      c    -1.000000E+21     9.856157E-03     1.000000E+21           
        294  traj.phases.phase0.control_group.indep_controls.controls:u_56      c    -1.000000E+21     1.249034E-02     1.000000E+21           
        295  traj.phases.phase0.control_group.indep_controls.controls:u_57      c    -1.000000E+21     1.343965E-02     1.000000E+21           
        296  traj.phases.phase0.control_group.indep_controls.controls:u_58      c    -1.000000E+21     1.591660E-02     1.000000E+21           
        297  traj.phases.phase0.control_group.indep_controls.controls:u_59      c    -1.000000E+21     2.012074E-02     1.000000E+21           
        298  traj.phases.phase0.control_group.indep_controls.controls:u_60      c    -1.000000E+21     2.164133E-02     1.000000E+21           
        299  traj.phases.phase0.control_group.indep_controls.controls:u_61      c    -1.000000E+21     2.560071E-02     1.000000E+21           
        300  traj.phases.phase0.control_group.indep_controls.controls:u_62      c    -1.000000E+21     3.228796E-02     1.000000E+21           
        301  traj.phases.phase0.control_group.indep_controls.controls:u_63      c    -1.000000E+21     3.470018E-02     1.000000E+21           
        302  traj.phases.phase0.control_group.indep_controls.controls:u_64      c    -1.000000E+21     4.100956E-02     1.000000E+21           
        303  traj.phases.phase0.control_group.indep_controls.controls:u_65      c    -1.000000E+21     5.176048E-02     1.000000E+21           
        304  traj.phases.phase0.control_group.indep_controls.controls:u_66      c    -1.000000E+21     5.565721E-02     1.000000E+21           
        305  traj.phases.phase0.control_group.indep_controls.controls:u_67      c    -1.000000E+21     6.580016E-02     1.000000E+21           
        306  traj.phases.phase0.control_group.indep_controls.controls:u_68      c    -1.000000E+21     8.290774E-02     1.000000E+21           
        307  traj.phases.phase0.control_group.indep_controls.controls:u_69      c    -1.000000E+21     8.907412E-02     1.000000E+21           
        308  traj.phases.phase0.control_group.indep_controls.controls:u_70      c    -1.000000E+21     1.052250E-01     1.000000E+21           
        309  traj.phases.phase0.control_group.indep_controls.controls:u_71      c    -1.000000E+21     1.328181E-01     1.000000E+21           
        310  traj.phases.phase0.control_group.indep_controls.controls:u_72      c    -1.000000E+21     1.428335E-01     1.000000E+21           
        311  traj.phases.phase0.control_group.indep_controls.controls:u_73      c    -1.000000E+21     1.688842E-01     1.000000E+21           
        312  traj.phases.phase0.control_group.indep_controls.controls:u_74      c    -1.000000E+21     2.127433E-01     1.000000E+21           
        313  traj.phases.phase0.control_group.indep_controls.controls:u_75      c    -1.000000E+21     2.285366E-01     1.000000E+21           
        314  traj.phases.phase0.control_group.indep_controls.controls:u_76      c    -1.000000E+21     2.699328E-01     1.000000E+21           
        315  traj.phases.phase0.control_group.indep_controls.controls:u_77      c    -1.000000E+21     3.407722E-01     1.000000E+21           
        316  traj.phases.phase0.control_group.indep_controls.controls:u_78      c    -1.000000E+21     3.665074E-01     1.000000E+21           
        317  traj.phases.phase0.control_group.indep_controls.controls:u_79      c    -1.000000E+21     4.334235E-01     1.000000E+21           
        318  traj.phases.phase0.control_group.indep_controls.controls:u_80      c    -1.000000E+21     5.459824E-01     1.000000E+21           
        319  traj.phases.phase0.control_group.indep_controls.controls:u_81      c    -1.000000E+21     5.864936E-01     1.000000E+21           
        320  traj.phases.phase0.control_group.indep_controls.controls:u_82      c    -1.000000E+21     6.926806E-01     1.000000E+21           
        321  traj.phases.phase0.control_group.indep_controls.controls:u_83      c    -1.000000E+21     8.744306E-01     1.000000E+21           
        322  traj.phases.phase0.control_group.indep_controls.controls:u_84      c    -1.000000E+21     9.404657E-01     1.000000E+21           
        323  traj.phases.phase0.control_group.indep_controls.controls:u_85      c    -1.000000E+21     1.112331E+00     1.000000E+21           
        324  traj.phases.phase0.control_group.indep_controls.controls:u_86      c    -1.000000E+21     1.401897E+00     1.000000E+21           
        325  traj.phases.phase0.control_group.indep_controls.controls:u_87      c    -1.000000E+21     1.506208E+00     1.000000E+21           
        326  traj.phases.phase0.control_group.indep_controls.controls:u_88      c    -1.000000E+21     1.779242E+00     1.000000E+21           
        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
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        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

  1. 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. ↩