def test_subspace_det_algo1_mimo(self):
"""
Subspace deterministic algorithm (MIMO).
"""
ss2 = sysid.StateSpaceDiscreteLinear(A=np.array([[0, 0.1, 0.2],
[0.2, 0.3, 0.4],
[0.4, 0.3, 0.2]]),
B=np.array([[1, 0], [0, 1],
[0, -1]]),
C=np.array([[1, 0, 0], [0, 1,
0]]),
D=np.array([[0, 0], [0, 0]]),
Q=np.diag([0.01, 0.01, 0.01]),
R=np.diag([0.01, 0.01]),
dt=0.1)
np.random.seed(1234)
prbs1 = sysid.prbs(1000)
prbs2 = sysid.prbs(1000)
def f_prbs_2d(t, x, i):
"input function"
#pylint: disable=unused-argument
i = i % 1000
return 2 * np.array([[prbs1[i] - 0.5], [prbs2[i] - 0.5]])
tf = 8
data = ss2.simulate(f_u=f_prbs_2d, x0=np.array([[0, 0, 0]]).T, tf=tf)
ss2_id = sysid.subspace_det_algo1(y=data.y,
u=data.u,
f=5,
p=5,
s_tol=0.1,
dt=ss2.dt)
data_id = ss2_id.simulate(
f_u=f_prbs_2d,
# x0=np.array(np.matrix(np.zeros(ss2_id.A.shape[0])).T),
x0=np.array([np.zeros(ss2_id.A.shape[0])]).T,
tf=tf)
nrms = sysid.nrms(data_id.y, data.y)
self.assertGreater(nrms, 0.9)
if ENABLE_PLOTTING:
for i in range(2):
plt.figure()
plt.plot(data_id.t.T,
data_id.y[i, :].T,
label='$y_{:d}$ true'.format(i))
plt.plot(data.t.T,
data.y[i, :].T,
label='$y_{:d}$ id'.format(i))
plt.legend()
plt.grid()
def test_subspace_det_algo1_siso(self):
"""
Subspace deterministic algorithm (SISO).
"""
ss1 = sysid.StateSpaceDiscreteLinear(
A=0.9, B=0.5, C=1, D=0, Q=0.01, R=0.01, dt=0.1)
pl.seed(1234)
prbs1 = sysid.prbs(1000)
def f_prbs(t, x, i):
"input function"
#pylint: disable=unused-argument, unused-variable
return prbs1[i]
tf = 10
data = ss1.simulate(f_u=f_prbs, x0=pl.matrix(0), tf=tf)
ss1_id = sysid.subspace_det_algo1(
y=data.y, u=data.u,
f=5, p=5, s_tol=1e-1, dt=ss1.dt)
data_id = ss1_id.simulate(f_u=f_prbs, x0=0, tf=tf)
nrms = sysid.subspace.nrms(data_id.y, data.y)
self.assertGreater(nrms, 0.9)
if ENABLE_PLOTTING:
pl.plot(data_id.t.T, data_id.x.T, label='id')
pl.plot(data.t.T, data.x.T, label='true')
pl.legend()
pl.grid()
def test_subspace_det_algo1_mimo(self):
"""
Subspace deterministic algorithm (MIMO).
"""
ss2 = sysid.StateSpaceDiscreteLinear(
A=pl.matrix([[0, 0.1, 0.2],
[0.2, 0.3, 0.4],
[0.4, 0.3, 0.2]]),
B=pl.matrix([[1, 0],
[0, 1],
[0, -1]]),
C=pl.matrix([[1, 0, 0],
[0, 1, 0]]),
D=pl.matrix([[0, 0],
[0, 0]]),
Q=pl.diag([0.01, 0.01, 0.01]), R=pl.diag([0.01, 0.01]), dt=0.1)
pl.seed(1234)
prbs1 = sysid.prbs(1000)
prbs2 = sysid.prbs(1000)
def f_prbs_2d(t, x, i):
"input function"
#pylint: disable=unused-argument
i = i%1000
return 2*pl.matrix([prbs1[i]-0.5, prbs2[i]-0.5]).T
tf = 8
data = ss2.simulate(
f_u=f_prbs_2d, x0=pl.matrix([0, 0, 0]).T, tf=tf)
ss2_id = sysid.subspace_det_algo1(
y=data.y, u=data.u,
f=5, p=5, s_tol=0.1, dt=ss2.dt)
data_id = ss2_id.simulate(
f_u=f_prbs_2d,
x0=pl.matrix(pl.zeros(ss2_id.A.shape[0])).T, tf=tf)
nrms = sysid.nrms(data_id.y, data.y)
self.assertGreater(nrms, 0.9)
if ENABLE_PLOTTING:
for i in range(2):
pl.figure()
pl.plot(data_id.t.T, data_id.y[i, :].T,
label='$y_{:d}$ true'.format(i))
pl.plot(data.t.T, data.y[i, :].T,
label='$y_{:d}$ id'.format(i))
pl.legend()
pl.grid()
def test_subspace_det_algo1_siso(self):
"""
Subspace deterministic algorithm (SISO).
"""
ss1 = sysid.StateSpaceDiscreteLinear(A=0.9,
B=0.5,
C=1,
D=0,
Q=0.01,
R=0.01,
dt=0.1)
np.random.seed(1234)
prbs1 = sysid.prbs(1000)
def f_prbs(t, x, i):
"input function"
# pylint: disable=unused-argument, unused-variable
return prbs1[i]
tf = 10
data = ss1.simulate(f_u=f_prbs, x0=np.matrix(0), tf=tf)
ss1_id = sysid.subspace_det_algo1(y=data.y,
u=data.u,
f=5,
p=5,
s_tol=1e-1,
dt=ss1.dt)
data_id = ss1_id.simulate(f_u=f_prbs, x0=0, tf=tf)
nrms = sysid.subspace.nrms(data_id.y, data.y)
self.assertGreater(nrms, 0.9)
if ENABLE_PLOTTING:
plt.plot(data_id.t.T, data_id.x.T, label='id')
plt.plot(data.t.T, data.x.T, label='true')
plt.legend()
plt.grid()
simulation_example = False
if simulation_example:
# 4 internal states MIMO [2 IN, 3 OUT]
ss3 = sysid.StateSpaceDiscreteLinear(
A=np.array([[0, 0.01, 0.2, 0.4], [0.1, 0.2, 0.2, 0.3], [0.11, 0.12, 0.21, 0.13], [0.11, 0.12, 0.21, 0.13]]), # X x X
B=np.array([[1, 0], [0, 1], [1, 0], [0, 1]]), # X x u
C=np.array([[1, 0, 0, 0], [0, 1, 0, 0], [0, 1, 0, 0]]), # y x x
D=np.array([[0, 0], [0, 0], [0, 0]]), # y x u
Q=np.diag([0.2, 0.1, 0.1, 0.1]), # X x X
R=np.diag([0.04, 0.04, 0.04]), # R? y x y
dt=0.1)
np.random.seed(1234)
prbs1 = sysid.prbs(1000)
prbs2 = sysid.prbs(1000)
prbs3 = sysid.prbs(1000)
def f_prbs_3d(t, x, i):
i = i%1000
return 2 * np.array([[prbs1[i]-0.5], [prbs2[i]-0.5]])
tf = 10
data3 = ss3.simulate(
f_u=f_prbs_3d,
x0=np.array([[0, 0, 0, 0]]).T,
tf=tf)
print(data3.u.shape, data3.y.shape, "shapes")
ss3_id = sysid.subspace_det_algo1(y=data3.y, u=data3.u,