Pyomo: Extending the "car ampl example" with additional constraints - pyomo

Question

After having seen the nice implementation of the "ampl car example" in Pyomo repository, I would like to keep extending the problem with new features and constraints, but I have found the next problems during development. Is someone able of fix them?
1) Added new constraint "electric car": Now the acceleration is limited by adherence until a determined speed and then constant power model is used. I am not able of implement this constraint as i would think. It is commented in the, but Pyomo complains about that a constraint is related to a variable. (now Umax depends of the car speed).
2) Added new comfort acceleration and jerk constraints. It seems they are working right, but should be nice if a Pyomo guru supervise them and tell me if they are really implemented in the correct way.
3) About last one, in order of reducing verbosity. Is there any way of combine accelerationL and accelerationU in a unique constraint? Same for jerkL and jerkU.
4) The last feature is a speed limit constraint divided in two steps. Again, I am not able of getting it works, so it is commented in code. Does anybody dare to fix it?
# Ampl Car Example (Extended)
#
# Shows how to convert a minimize final time optimal control problem
# to a format pyomo.dae can handle by removing the time scaling from
# the ContinuousSet.
#
# min tf
# dx/dt = v
# dv/dt = u - R*v^2
# x(0)=0; x(tf)=L
# v(0)=0; v(tf)=0
# -3 <= u <= 1 (engine constraint)
#
# {v <= 7m/s ===> u < 1
# u <= { (electric car constraint)
# {v > 7m/s ===> u < 1*7/v
#
# -1.5 <= dv/dt <= 0.8 (comfort constraint -> smooth driving)
# -0.5 <= d2v/dt2 <= 0.5 (comfort constraint -> jerk)
# v <= Vmax (40 kmh[0-500m] + 25 kmh(500-1000m])
from pyomo.environ import *
from pyomo.dae import *
m = ConcreteModel()
m.R = Param(initialize=0.001) # Friction factor
m.L = Param(initialize=1000.0) # Final position
m.T = Param(initialize=50.0) # Estimated time
m.aU = Param(initialize=0.8) # Acceleration upper bound
m.aL = Param(initialize=-1.5) # Acceleration lower bound
m.jU = Param(initialize=0.5) # Jerk upper bound
m.jL = Param(initialize=-0.5) # Jerk lower bound
m.NFE = Param(initialize=100) # Number of finite elements
'''
def _initX(m, i):
return m.x[i] == i*m.L/m.NFE
def _initV(m):
return m.v[i] == m.L/50
'''
m.tf = Var()
m.tau = ContinuousSet(bounds=(0,1)) # Unscaled time
m.t = Var(m.tau) # Scaled time
m.x = Var(m.tau, bounds=(0,m.L))
m.v = Var(m.tau, bounds=(0,None))
m.u = Var(m.tau, bounds=(-3,1), initialize=0)
m.dt = DerivativeVar(m.t)
m.dx = DerivativeVar(m.x)
m.dv = DerivativeVar(m.v)
m.da = DerivativeVar(m.v, wrt=(m.tau, m.tau))
m.obj = Objective(expr=m.tf)
def _ode1(m, i):
if i==0:
return Constraint.Skip
return m.dt[i] == m.tf
m.ode1 = Constraint(m.tau, rule=_ode1)
def _ode2(m, i):
if i==0:
return Constraint.Skip
return m.dx[i] == m.tf * m.v[i]
m.ode2 = Constraint(m.tau, rule=_ode2)
def _ode3(m, i):
if i==0:
return Constraint.Skip
return m.dv[i] == m.tf*(m.u[i] - m.R*m.v[i]**2)
m.ode3 = Constraint(m.tau, rule=_ode3)
def _accelerationL(m, i):
if i==0:
return Constraint.Skip
return m.dv[i] >= m.aL*m.tf
m.accelerationL = Constraint(m.tau, rule=_accelerationL)
def _accelerationU(m, i):
if i==0:
return Constraint.Skip
return m.dv[i] <= m.aU*m.tf
m.accelerationU = Constraint(m.tau, rule=_accelerationU)
def _jerkL(m, i):
if i==0:
return Constraint.Skip
return m.da[i] >= m.jL*m.tf**2
m.jerkL = Constraint(m.tau, rule=_jerkL)
def _jerkU(m, i):
if i==0:
return Constraint.Skip
return m.da[i] <= m.jU*m.tf**2
m.jerkU = Constraint(m.tau, rule=_jerkU)
'''
def _electric(m, i):
if i==0:
return Constraint.Skip
elif value(m.v[i])<=7:
return m.a[i] <= 1
else:
return m.v[i] <= 1*7/m.v[i]
m.electric = Constraint(m.tau, rule=_electric)
'''
'''
def _speed(m, i):
if i==0:
return Constraint.Skip
elif value(m.x[i])<=500:
return m.v[i] <= 40/3.6
else:
return m.v[i] <= 25/3.6
m.speed = Constraint(m.tau, rule=_speed)
'''
def _initial(m):
yield m.x[0] == 0
yield m.x[1] == m.L
yield m.v[0] == 0
yield m.v[1] == 0
yield m.t[0] == 0
m.initial = ConstraintList(rule=_initial)
discretizer = TransformationFactory('dae.finite_difference')
discretizer.apply_to(m, nfe=value(m.NFE), wrt=m.tau, scheme='BACKWARD')
#discretizer = TransformationFactory('dae.collocation')
#discretizer.apply_to(m, nfe=value(m.NFE), ncp=4, wrt=m.tau, scheme='LAGRANGE-RADAU')
solver = SolverFactory('ipopt')
solver.solve(m,tee=True)
print("final time = %6.2f" %(value(m.tf)))
t = []
x = []
v = []
a = []
u = []
for i in m.tau:
t.append(value(m.t[i]))
x.append(value(m.x[i]))
v.append(3.6*value(m.v[i]))
a.append(10*value(m.u[i] - m.R*m.v[i]**2))
u.append(10*value(m.u[i]))
import matplotlib.pyplot as plt
plt.plot(x, v, label='v (km/h)')
plt.plot(x, a, label='a (dm/s2)')
plt.plot(x, u, label='u (dm/s2)')
plt.xlabel('distance')
plt.grid('on')
plt.legend()
plt.show()
Thanks a lot in advance,
Pablo

Answer 1

(1) You should not think of Pyomo constraint rules as callbacks that are used by the solver. You should think of them more as a function to generate a container of constraint objects that gets called once for each index when the model is constructed. Meaning it is invalid to use a variable in an if statement unless you are really only using its initial value to define the constraint expression. There are ways to express what I think you are trying to do, but they involve introducing binary variables into the problem, in which case you can no longer use Ipopt.
(2) Can't really provide any help. Syntax looks fine.
(3) Pyomo allows you to return double-sided inequality expressions (e.g., L <= f(x) <= U) from constraint rules, but they can not involve variable expressions in the L and U locations. It doesn't look like the constraints you are referring to can be combined into this form.
(4) See (1)