```
"""
system description: brokett-integrator: second order
polynomial, three state components, two affine inputs, no drift
problem specification for control problem: brokett-integrator does not admit a continuously differentiable control
law
"""
import numpy as np
import sympy as sp
from sympy import cos, sin, symbols
from math import pi
from ackrep_core import ResultContainer
from system_models.brockett_integrator_system.system_model import Model
import symbtools as st
from ipydex import IPS
class ProblemSpecification(object):
# system symbols for setting up the equation of motion
model = Model()
x1, x2, x3 = model.xx_symb
xx = sp.Matrix(model.xx_symb) # states of system
u = model.uu_symb # input of system
zz = st.symb_vector("z1:4")
vv = st.symb_vector("v1:3")
@classmethod
def rhs(cls):
"""
:return: symbolic rhs-functions
"""
return sp.Matrix(cls.model.get_rhs_symbolic())
def evaluate_solution(solution_data):
"""
:param solution_data: solution data of problem of solution
:return: ResultContainer
"""
expected_final_state = [
0.009998614859126023,
0.009957360996513998,
0.009967762399005667,
0.009978835190223072,
0.009952036758485753,
0.009919577816086893,
0.009980123216488885,
0.009949576326506008,
0.009914913316709522,
0.009953621346320544,
0.009988298247260814,
0.009967790153907679,
0.009991916470644626,
0.00999680390155051,
0.009916822160298005,
0.009918459738891074,
0.00989244893289128,
0.009845376127559528,
0.009974183969899204,
0.009887464353824928,
]
rc = ResultContainer(score=1.0)
simulated_final_state = []
for i in range(len(solution_data)):
simulated_final_state.append(solution_data[i][-1][-1])
rc.final_state_errors = [
simulated_final_state[i] - expected_final_state[i] for i in np.arange(0, len(simulated_final_state))
]
rc.success = np.allclose(expected_final_state, simulated_final_state, rtol=0, atol=1e-2)
return rc
```

controller design for the brockett-integrator

brockett integrator