def solve13():
# Optimization of Multiple Linked Phases
# Initialize gekko model
m = GEKKO()
# Number of collocation nodes
nodes = 3
# Number of phases
n = 5
# Time horizon (for all phases)
m.time = np.linspace(0, 1, 100)
# Input (constant in IMODE 4)
u = [m.Var(1, lb=-2, ub=2, fixed_initial=False) for i in range(n)]
# Example of same parameter for each phase
tau = 5
# Example of different parameters for each phase
K = [2, 3, 5, 1, 4]
# Scale time of each phase
tf = [1, 2, 4, 8, 16]
# Variables (one version of x for each phase)
x = [m.Var(0) for i in range(5)]
# Equations (different for each phase)
for i in range(n):
m.Equation(tau * x[i].dt() / tf[i] == -x[i] + K[i] * u[i])
# Connect phases together at endpoints
for i in range(n - 1):
m.Connection(x[i + 1], x[i], 1, len(m.time) - 1, 1, nodes)
m.Connection(x[i + 1], 'CALCULATED', pos1=1, node1=1)
# Objective
# Maximize final x while keeping third phase = -1
m.Obj(-x[n - 1] + (x[2] + 1)**2 * 100)
# Solver options
m.options.IMODE = 6
m.options.NODES = nodes
# Solve
m.solve()
# Calculate the start time of each phase
ts = [0]
for i in range(n - 1):
ts.append(ts[i] + tf[i])
# Plot
plt.figure()
tm = np.empty(len(m.time))
for i in range(n):
tm = m.time * tf[i] + ts[i]
plt.plot(tm, x[i])
plt.show()
c = 17.5 r = 0.71 k = 80.5 U_max = 20 u = m.MV(lb=0, ub=1, value=1) u.STATUS = 1 x = m.Var(value=70) m.Equation(x.dt() == r * x * (1 - x / k) - u * U_max) J = m.Var(value=0) Jf = m.FV() Jf.STATUS = 1 m.Connection(Jf, J, pos2='end') m.Equation(J.dt() == (E - c / x) * u * U_max) m.Obj(-Jf) m.options.IMODE = 6 m.options.NODES = 3 m.options.SOLVER = 3 m.solve(debug=True) #m.GUI() print(Jf.value[0]) plt.figure() plt.subplot(2, 1, 1) plt.plot(m.time, J.value, label='$')
class MPCnode(Node):
def __init__(self, id, x, y, nrj, ctrlHrz, ctrlRes):
super().__init__(id, x, y, nrj)
self.verbose = True
self.ctrlHrz = ctrlHrz # Control Horizon
# time points
self.ctrlRes = ctrlRes # Control Resolution. Number of control steps within the control horizon
# constants
self.Egen = 1*10**-5
self.const = 0.6
self.packet = 1
self.E = 1
self.m = GEKKO(remote=False)
self.m.time = np.linspace( 0, self.ctrlHrz, self.ctrlRes)
#self.deltaDist = -1.5
self.deltaDist = self.m.FV(value = -1.5)
#self.deltaDist.STATUS = 1
# packet rate
self.pr = self.m.MV(value=self.PA, integer = True,lb=1,ub=20)
self.pr.STATUS = 1
self.pr.DCOST = 0
# Energy Stored
self.nrj = self.m.Var(value=0.05, lb=0) # Energy Amount
self.d = self.m.Var(value=70, lb = 0) # Distance to receiver
self.d2 = self.m.Intermediate(self.d**2)
# energy/pr balance
#self.m.Equation(self.d.dt() == -1.5)
self.m.Equation(self.d.dt() == self.deltaDist)
self.m.Equation(self.nrj >= self.Egen - ((Eelec+EDA)*self.packet + self.pr*self.pSize*(Eelec + Eamp * self.d2)))
self.m.Equation(self.nrj.dt() == self.Egen - ((Eelec+EDA)*self.packet + self.pr*self.pSize*(Eelec + Eamp * self.d2)))
# objective (profit)
self.J = self.m.Var(value=0)
# final objective
self.Jf = self.m.FV()
self.Jf.STATUS = 1
self.m.Connection(self.Jf,self.J,pos2='end')
self.m.Equation(self.J.dt() == self.pr*self.pSize)
# maximize profit
self.m.Obj(-self.Jf)
# options
self.m.options.IMODE = 6 # optimal control
self.m.options.NODES = 3 # collocation nodes
self.m.options.SOLVER = 1 # solver (IPOPT)
def resetGEKKO(self):
self.m = GEKKO(remote=False)
self.m.time = np.linspace( 0, self.ctrlHrz, self.ctrlRes)
self.pr = self.m.MV(value=self.PA, integer = True,lb=1,ub=20)
self.pr.STATUS = 1
self.pr.DCOST = 0
def getDeltaDist(self, sinkX, sinkY, sdeltaX, sdeltaY, deltaDist):
distBefore = np.sqrt((sinkX**2)+(sinkY**2))
distAfter = np.sqrt(((sinkX+sdeltaX)**2)+((sinkY+sdeltaY)**2))
self.deltaDist = distAfter - distBefore
return self.deltaDist
def controlPR(self, deltaD):
# solve optimization problem
self.deltaDist.value = 1.5
self.m.solve(disp=False)
self.setPR(self.pr.value[1])
#self.pr.value = self.pr.value[1]
#self.m.GUI()
# print profit
print('Optimal Profit: ' + str(self.Jf.value[0]))
if self.verbose:
# plot results
plt.figure(1)
plt.subplot(2,1,1)
plt.plot(self.m.time,self.J.value,'r--',label='packets')
plt.plot(self.m.time[-1],self.Jf.value[0],'ro',markersize=10,\
label='final packets = '+str(self.Jf.value[0]))
plt.plot(self.m.time,self.nrj.value,'b-',label='energy')
plt.ylabel('Value')
plt.legend()
plt.subplot(2,1,2)
plt.plot(self.m.time,self.pr.value,'k.-',label='packet rate')
plt.ylabel('Rate')
plt.xlabel('Time (yr)')
plt.legend()
plt.show()
u = m.MV(value=1, lb=0, ub=1) u.STATUS = 1 u.DCOST = 0 # population x = m.Var(70) # population balance m.Equation(x.dt() == r * x * (1 - x/k) - u*u_max) # profit j = m.Var(value=0) # objective jF = m.FV() # final objective jF.STATUS = 1 m.Connection(jF, j, pos2 = 'end') m.Equation(j.dt() == (e - c / x) * u * u_max) m.Obj(-j) m.options.IMODE = 6 # optimal control mode m.options.NODES = 3 m.options.SOLVER = 3 m.solve(disp=False) print(jF.value[0]) plt.figure(1) # plot results plt.subplot(2,1,1) plt.plot(m.time,j.value,'r--',label='profit')
def fishing():
m = GEKKO()
n = 101
m.time = np.linspace(0, 10, n)
E = 1
c = 17.5
r = 0.71
k = 80.5
U_max = 20
u = m.MV(lb=0, ub=1, value=1)
u.STATUS = 1
x = m.Var(value=70)
m.Equation(x.dt() == r * x * (1 - x / k) - u * U_max)
J = m.Var(value=0)
Jf = m.FV()
Jf.STATUS = 1
m.Connection(Jf, J, pos2='end')
m.Equation(J.dt() == (E - c / x) * u * U_max)
m.Obj(-Jf)
m.options.IMODE = 6
m.options.NODES = 3
m.options.SOLVER = 3
m.solve(disp=False)
assert J.value == [
0.0, 1.495191, 2.980856, 4.45711, 5.924057, 7.381791, 8.830394,
10.26994, 11.70049, 13.1221, 14.5348, 15.93865, 17.33365, 18.71983,
20.0972, 21.46575, 22.82547, 24.17635, 25.51835, 26.85144, 28.17557,
29.49069, 30.79672, 32.09258, 33.19262, 34.14704, 35.03382, 35.90079,
36.7674, 37.63793, 38.51146, 39.38639, 40.26171, 41.13703, 42.01228,
42.88747, 43.76263, 44.63778, 45.51293, 46.38808, 47.26324, 48.13839,
49.01354, 49.88869, 50.76384, 51.63899, 52.51415, 53.3893, 54.26445,
55.1396, 56.01475, 56.88991, 57.76506, 58.64021, 59.51536, 60.39051,
61.26566, 62.14082, 63.01597, 63.89114, 64.76636, 65.64164, 66.51694,
67.39212, 68.2665, 69.13882, 70.00774, 70.87441, 71.74908, 72.66269,
73.67438, 74.84509, 76.11564, 77.37664, 78.62796, 79.86948, 81.10102,
82.32241, 83.53349, 84.73404, 85.92385, 87.10269, 88.2703, 89.4264,
90.57071, 91.70289, 92.82261, 93.92949, 95.02312, 96.10307, 97.16886,
98.21996, 99.25584, 100.2759, 101.2794, 102.2657, 103.2339, 104.1833,
105.1128, 106.0215, 106.9081
]
assert Jf.value == [
106.9081, 106.9081, 106.9081, 106.9081, 106.9081, 106.9081, 106.9081,
106.9081, 106.9081, 106.9081, 106.9081, 106.9081, 106.9081, 106.9081,
106.9081, 106.9081, 106.9081, 106.9081, 106.9081, 106.9081, 106.9081,
106.9081, 106.9081, 106.9081, 106.9081, 106.9081, 106.9081, 106.9081,
106.9081, 106.9081, 106.9081, 106.9081, 106.9081, 106.9081, 106.9081,
106.9081, 106.9081, 106.9081, 106.9081, 106.9081, 106.9081, 106.9081,
106.9081, 106.9081, 106.9081, 106.9081, 106.9081, 106.9081, 106.9081,
106.9081, 106.9081, 106.9081, 106.9081, 106.9081, 106.9081, 106.9081,
106.9081, 106.9081, 106.9081, 106.9081, 106.9081, 106.9081, 106.9081,
106.9081, 106.9081, 106.9081, 106.9081, 106.9081, 106.9081, 106.9081,
106.9081, 106.9081, 106.9081, 106.9081, 106.9081, 106.9081, 106.9081,
106.9081, 106.9081, 106.9081, 106.9081, 106.9081, 106.9081, 106.9081,
106.9081, 106.9081, 106.9081, 106.9081, 106.9081, 106.9081, 106.9081,
106.9081, 106.9081, 106.9081, 106.9081, 106.9081, 106.9081, 106.9081,
106.9081, 106.9081, 106.9081
]
assert x.value == [
70.0, 68.68286, 67.43015, 66.23608, 65.0955, 64.00383, 62.95696,
61.95118, 60.98318, 60.04994, 59.14873, 58.27707, 57.43269, 56.61351,
55.81765, 55.04334, 54.28897, 53.55306, 52.83422, 52.13115, 51.44267,
50.76765, 50.10503, 49.45505, 49.10604, 48.98275, 48.96466, 48.97739,
48.99067, 48.99787, 49.00039, 49.00074, 49.00047, 49.00021, 49.00006,
49.0, 48.99999, 48.99999, 48.99999, 48.99999, 49.0, 49.0, 49.0, 49.0,
49.0, 49.0, 49.0, 49.0, 49.0, 49.0, 49.0, 49.0, 49.0, 49.0, 49.00001,
49.00001, 49.00001, 49.00001, 49.0, 48.99997, 48.99987, 48.99967,
48.99944, 48.9994, 49.0006, 49.005, 49.0147, 49.02789, 49.02863,
48.96884, 48.75625, 48.29394, 47.6701, 47.05438, 46.44599, 45.84423,
45.24837, 44.65774, 44.07168, 43.48957, 42.91077, 42.33468, 41.7607,
41.18826, 40.61676, 40.04563, 39.47429, 38.90217, 38.32869, 37.75326,
37.17529, 36.59418, 36.00931, 35.42005, 34.82575, 34.22573, 33.6193,
33.00574, 32.38429, 31.75415, 31.1145
]
assert u.value == [
1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.853423, 0.7421807,
0.6899773, 0.6745367, 0.674141, 0.6771105, 0.6794158, 0.6804968,
0.6808019, 0.6808022, 0.6807487, 0.6807017, 0.6806795, 0.6806744,
0.6806733, 0.680673, 0.680673, 0.6806731, 0.6806734, 0.6806735,
0.6806737, 0.6806738, 0.6806739, 0.6806739, 0.6806738, 0.6806737,
0.6806736, 0.6806735, 0.6806733, 0.6806732, 0.6806732, 0.6806732,
0.6806735, 0.6806743, 0.6806769, 0.6806896, 0.6807248, 0.6807767,
0.6807916, 0.6806986, 0.6800795, 0.6784639, 0.6757571, 0.6738888,
0.6799703, 0.710282, 0.7875389, 0.9150895, 1.0, 1.0, 1.0, 1.0, 1.0,
1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0
]
