#  _________________________________________________________________________
#
#  Pyomo: Python Optimization Modeling Objects
#  Copyright (c) 2014 Sandia Corporation.
#  Under the terms of Contract DE-AC04-94AL85000 with Sandia Corporation,
#  the U.S. Government retains certain rights in this software.
#  This software is distributed under the BSD License.
#  _________________________________________________________________________

# Sample Problem 1 (Ex 1 from Dynopt Guide)
#
#	min X2(tf)
#	s.t.	X1_dot = u			X1(0) = 1
#		X2_dot = X1^2 + u^2		X2(0) = 0
#		tf = 1

from pyomo.environ import *
from pyomo.dae import *

m = ConcreteModel()

m.t = ContinuousSet(bounds=(0,1)) 

m.x1 = Var(m.t, bounds=(0,1))
m.x2 = Var(m.t, bounds=(0,1))
m.u = Var(m.t, initialize=0)

m.x1dot = DerivativeVar(m.x1)
m.x2dot = DerivativeVar(m.x2)

m.obj = Objective(expr=m.x2[1])

def _x1dot(M,i):
	if i == 0:
		return Constraint.Skip
	return M.x1dot[i] == M.u[i]
m.x1dotcon = Constraint(m.t, rule=_x1dot)

def _x2dot(M,i):
	if i == 0:
		return Constraint.Skip
	return M.x2dot[i] == M.x1[i]**2 + M.u[i]**2
m.x2dotcon = Constraint(m.t, rule=_x2dot)

def _init(M):
	yield M.x1[0] == 1
	yield M.x2[0] == 0
	yield ConstraintList.End
m.init_conditions = ConstraintList(rule=_init)

